diff --git a/lib/applyEach.js b/lib/applyEach.js
index d1dfc7889..93d8af3cd 100644
--- a/lib/applyEach.js
+++ b/lib/applyEach.js
@@ -13,7 +13,7 @@ import map from './map';
  * @memberOf module:ControlFlow
  * @method
  * @category Control Flow
- * @param {Array|Iterable|Object} fns - A collection of asynchronous functions
+ * @param {Array|Iterable|Object} fns - A collection of {@link AsyncFunction}s
  * to all call with the same arguments
  * @param {...*} [args] - any number of separate arguments to pass to the
  * function.
diff --git a/lib/applyEachSeries.js b/lib/applyEachSeries.js
index 5a7c257bf..392b1396e 100644
--- a/lib/applyEachSeries.js
+++ b/lib/applyEachSeries.js
@@ -10,7 +10,7 @@ import mapSeries from './mapSeries';
  * @method
  * @see [async.applyEach]{@link module:ControlFlow.applyEach}
  * @category Control Flow
- * @param {Array|Iterable|Object} fns - A collection of asynchronous functions to all
+ * @param {Array|Iterable|Object} fns - A collection of {@link AsyncFunction}s to all
  * call with the same arguments
  * @param {...*} [args] - any number of separate arguments to pass to the
  * function.
diff --git a/lib/asyncify.js b/lib/asyncify.js
index 1f0955e5f..96eea543b 100644
--- a/lib/asyncify.js
+++ b/lib/asyncify.js
@@ -20,10 +20,10 @@ import initialParams from './internal/initialParams';
  * @method
  * @alias wrapSync
  * @category Util
- * @param {Function} func - The synchronous function to convert to an
- * asynchronous function.
- * @returns {Function} An asynchronous wrapper of the `func`. To be invoked with
- * (callback).
+ * @param {Function} func - The synchronous funuction, or Promise-returning
+ * function to convert to an {@link AsyncFunction}.
+ * @returns {AsyncFunction} An asynchronous wrapper of the `func`. To be
+ * invoked with `(args..., callback)`.
  * @example
  *
  * // passing a regular synchronous function
diff --git a/lib/auto.js b/lib/auto.js
index 4d7bf32d3..ba0fdc337 100644
--- a/lib/auto.js
+++ b/lib/auto.js
@@ -11,17 +11,17 @@ import onlyOnce from './internal/onlyOnce';
 import wrapAsync from './internal/wrapAsync';
 
 /**
- * Determines the best order for running the functions in `tasks`, based on
+ * Determines the best order for running the {@link AsyncFunction}s in `tasks`, based on
  * their requirements. Each function can optionally depend on other functions
  * being completed first, and each function is run as soon as its requirements
  * are satisfied.
  *
- * If any of the functions pass an error to their callback, the `auto` sequence
+ * If any of the {@link AsyncFunction}s pass an error to their callback, the `auto` sequence
  * will stop. Further tasks will not execute (so any other functions depending
  * on it will not run), and the main `callback` is immediately called with the
  * error.
  *
- * Functions also receive an object containing the results of functions which
+ * {@link AsyncFunction}s also receive an object containing the results of functions which
  * have completed so far as the first argument, if they have dependencies. If a
  * task function has no dependencies, it will only be passed a callback.
  *
@@ -31,7 +31,7 @@ import wrapAsync from './internal/wrapAsync';
  * @method
  * @category Control Flow
  * @param {Object} tasks - An object. Each of its properties is either a
- * function or an array of requirements, with the function itself the last item
+ * function or an array of requirements, with the {@link AsyncFunction} itself the last item
  * in the array. The object's key of a property serves as the name of the task
  * defined by that property, i.e. can be used when specifying requirements for
  * other tasks. The function receives one or two arguments:
diff --git a/lib/autoInject.js b/lib/autoInject.js
index 3ba87fcc5..bc8ddd6ef 100644
--- a/lib/autoInject.js
+++ b/lib/autoInject.js
@@ -40,7 +40,7 @@ function parseParams(func) {
  * @method
  * @see [async.auto]{@link module:ControlFlow.auto}
  * @category Control Flow
- * @param {Object} tasks - An object, each of whose properties is a function of
+ * @param {Object} tasks - An object, each of whose properties is an {@link AsyncFunction} of
  * the form 'func([dependencies...], callback). The object's key of a property
  * serves as the name of the task defined by that property, i.e. can be used
  * when specifying requirements for other tasks.
diff --git a/lib/cargo.js b/lib/cargo.js
index d86cb67b6..5060223fa 100644
--- a/lib/cargo.js
+++ b/lib/cargo.js
@@ -48,9 +48,8 @@ import queue from './internal/queue';
  * @method
  * @see [async.queue]{@link module:ControlFlow.queue}
  * @category Control Flow
- * @param {Function} worker - An asynchronous function for processing an array
- * of queued tasks, which must call its `callback(err)` argument when finished,
- * with an optional `err` argument. Invoked with `(tasks, callback)`.
+ * @param {AsyncFunction} worker - An asynchronous function for processing an array
+ * of queued tasks. Invoked with `(tasks, callback)`.
  * @param {number} [payload=Infinity] - An optional `integer` for determining
  * how many tasks should be processed per round; if omitted, the default is
  * unlimited.
diff --git a/lib/compose.js b/lib/compose.js
index 5c64593f6..96632c05b 100644
--- a/lib/compose.js
+++ b/lib/compose.js
@@ -14,7 +14,7 @@ import rest from './internal/rest';
  * @memberOf module:ControlFlow
  * @method
  * @category Control Flow
- * @param {...Function} functions - the asynchronous functions to compose
+ * @param {...AsyncFunction} functions - the asynchronous functions to compose
  * @returns {Function} an asynchronous function that is the composed
  * asynchronous `functions`
  * @example
diff --git a/lib/concat.js b/lib/concat.js
index ba4ea1314..7edf75937 100644
--- a/lib/concat.js
+++ b/lib/concat.js
@@ -14,10 +14,8 @@ import doParallel from './internal/doParallel';
  * @method
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A function to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, results)` which must be called once
- * it has completed with an error (which can be `null`) and an array of results.
- * Invoked with (item, callback).
+ * @param {AsyncFunction} iteratee - A function to apply to each item in `coll`,
+ * which should use an array as its result. Invoked with (item, callback).
  * @param {Function} [callback(err)] - A callback which is called after all the
  * `iteratee` functions have finished, or an error occurs. Results is an array
  * containing the concatenated results of the `iteratee` function. Invoked with
diff --git a/lib/concatSeries.js b/lib/concatSeries.js
index 77b439bc8..f5b3fab9c 100644
--- a/lib/concatSeries.js
+++ b/lib/concatSeries.js
@@ -11,9 +11,8 @@ import doSeries from './internal/doSeries';
  * @see [async.concat]{@link module:Collections.concat}
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A function to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, results)` which must be called once
- * it has completed with an error (which can be `null`) and an array of results.
+ * @param {AsyncFunction} iteratee - A function to apply to each item in `coll`.
+ * The iteratee should complete with an array an array of results.
  * Invoked with (item, callback).
  * @param {Function} [callback(err)] - A callback which is called after all the
  * `iteratee` functions have finished, or an error occurs. Results is an array
diff --git a/lib/constant.js b/lib/constant.js
index c9c0c1e72..ae6ffd099 100644
--- a/lib/constant.js
+++ b/lib/constant.js
@@ -13,7 +13,7 @@ import initialParams from './internal/initialParams';
  * @category Util
  * @param {...*} arguments... - Any number of arguments to automatically invoke
  * callback with.
- * @returns {Function} Returns a function that when invoked, automatically
+ * @returns {AsyncFunction} Returns a function that when invoked, automatically
  * invokes the callback with the previous given arguments.
  * @example
  *
diff --git a/lib/detect.js b/lib/detect.js
index 5f5a7ef9f..654a370fa 100644
--- a/lib/detect.js
+++ b/lib/detect.js
@@ -21,9 +21,9 @@ import findGetResult from './internal/findGetResult';
  * @alias find
  * @category Collections
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A truth test to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, truthValue)` which must be called
- * with a boolean argument once it has completed. Invoked with (item, callback).
+ * @param {AsyncFunction} iteratee - A truth test to apply to each item in `coll`.
+ * The iteratee must complete with a boolean value as its result.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called as soon as any
  * iteratee returns `true`, or after all the `iteratee` functions have finished.
  * Result will be the first item in the array that passes the truth test
diff --git a/lib/detectLimit.js b/lib/detectLimit.js
index d0f2a92af..bba10c839 100644
--- a/lib/detectLimit.js
+++ b/lib/detectLimit.js
@@ -17,9 +17,9 @@ import findGetResult from './internal/findGetResult';
  * @category Collections
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
  * @param {number} limit - The maximum number of async operations at a time.
- * @param {Function} iteratee - A truth test to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, truthValue)` which must be called
- * with a boolean argument once it has completed. Invoked with (item, callback).
+ * @param {AsyncFunction} iteratee - A truth test to apply to each item in `coll`.
+ * The iteratee must complete with a boolean value as its result.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called as soon as any
  * iteratee returns `true`, or after all the `iteratee` functions have finished.
  * Result will be the first item in the array that passes the truth test
diff --git a/lib/detectSeries.js b/lib/detectSeries.js
index 51413df39..684bdaaab 100644
--- a/lib/detectSeries.js
+++ b/lib/detectSeries.js
@@ -12,9 +12,9 @@ import doLimit from './internal/doLimit';
  * @alias findSeries
  * @category Collections
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A truth test to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, truthValue)` which must be called
- * with a boolean argument once it has completed. Invoked with (item, callback).
+ * @param {AsyncFunction} iteratee - A truth test to apply to each item in `coll`.
+ * The iteratee must complete with a boolean value as its result.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called as soon as any
  * iteratee returns `true`, or after all the `iteratee` functions have finished.
  * Result will be the first item in the array that passes the truth test
diff --git a/lib/dir.js b/lib/dir.js
index 912b558ae..8a5b5e3ee 100644
--- a/lib/dir.js
+++ b/lib/dir.js
@@ -1,10 +1,11 @@
 import consoleFunc from './internal/consoleFunc';
 
 /**
- * Logs the result of an `async` function to the `console` using `console.dir`
- * to display the properties of the resulting object. Only works in Node.js or
- * in browsers that support `console.dir` and `console.error` (such as FF and
- * Chrome). If multiple arguments are returned from the async function,
+ * Logs the result of an [`async` function]{@link AsyncFunction} to the
+ * `console` using `console.dir` to display the properties of the resulting object.
+ * Only works in Node.js or in browsers that support `console.dir` and
+ * `console.error` (such as FF and Chrome).
+ * If multiple arguments are returned from the async function,
  * `console.dir` is called on each argument in order.
  *
  * @name dir
@@ -12,8 +13,8 @@ import consoleFunc from './internal/consoleFunc';
  * @memberOf module:Utils
  * @method
  * @category Util
- * @param {Function} function - The function you want to eventually apply all
- * arguments to.
+ * @param {AsyncFunction} function - The function you want to eventually apply
+ * all arguments to.
  * @param {...*} arguments... - Any number of arguments to apply to the function.
  * @example
  *
diff --git a/lib/doDuring.js b/lib/doDuring.js
index e79574b55..7b52c22c2 100644
--- a/lib/doDuring.js
+++ b/lib/doDuring.js
@@ -14,10 +14,9 @@ import wrapAsync from './internal/wrapAsync';
  * @method
  * @see [async.during]{@link module:ControlFlow.during}
  * @category Control Flow
- * @param {Function} fn - A function which is called each time `test` passes.
- * The function is passed a `callback(err)`, which must be called once it has
- * completed with an optional `err` argument. Invoked with (callback).
- * @param {Function} test - asynchronous truth test to perform before each
+ * @param {AsyncFunction} fn - An async function which is called each time
+ * `test` passes. Invoked with (callback).
+ * @param {AsyncFunction} test - asynchronous truth test to perform before each
  * execution of `fn`. Invoked with (...args, callback), where `...args` are the
  * non-error args from the previous callback of `fn`.
  * @param {Function} [callback] - A callback which is called after the test
diff --git a/lib/doUntil.js b/lib/doUntil.js
index 0c5bb7194..06d3af77f 100644
--- a/lib/doUntil.js
+++ b/lib/doUntil.js
@@ -10,18 +10,18 @@ import doWhilst from './doWhilst';
  * @method
  * @see [async.doWhilst]{@link module:ControlFlow.doWhilst}
  * @category Control Flow
- * @param {Function} fn - A function which is called each time `test` fails.
- * The function is passed a `callback(err)`, which must be called once it has
- * completed with an optional `err` argument. Invoked with (callback).
+ * @param {AsyncFunction} iteratee - An async function which is called each time
+ * `test` fails. Invoked with (callback).
  * @param {Function} test - synchronous truth test to perform after each
- * execution of `fn`. Invoked with the non-error callback results of `fn`.
+ * execution of `iteratee`. Invoked with any non-error callback results of
+ * `iteratee`.
  * @param {Function} [callback] - A callback which is called after the test
- * function has passed and repeated execution of `fn` has stopped. `callback`
- * will be passed an error and any arguments passed to the final `fn`'s
+ * function has passed and repeated execution of `iteratee` has stopped. `callback`
+ * will be passed an error and any arguments passed to the final `iteratee`'s
  * callback. Invoked with (err, [results]);
  */
-export default function doUntil(fn, test, callback) {
-    doWhilst(fn, function() {
+export default function doUntil(iteratee, test, callback) {
+    doWhilst(iteratee, function() {
         return !test.apply(this, arguments);
     }, callback);
 }
diff --git a/lib/doWhilst.js b/lib/doWhilst.js
index 39f460008..4407305f6 100644
--- a/lib/doWhilst.js
+++ b/lib/doWhilst.js
@@ -16,11 +16,10 @@ import wrapAsync from './internal/wrapAsync';
  * @method
  * @see [async.whilst]{@link module:ControlFlow.whilst}
  * @category Control Flow
- * @param {Function} iteratee - A function which is called each time `test`
- * passes. The function is passed a `callback(err)`, which must be called once
- * it has completed with an optional `err` argument. Invoked with (callback).
+ * @param {AsyncFunction} iteratee - A function which is called each time `test`
+ * passes. Invoked with (callback).
  * @param {Function} test - synchronous truth test to perform after each
- * execution of `iteratee`. Invoked with the non-error callback results of
+ * execution of `iteratee`. Invoked with any non-error callback results of
  * `iteratee`.
  * @param {Function} [callback] - A callback which is called after the test
  * function has failed and repeated execution of `iteratee` has stopped.
diff --git a/lib/during.js b/lib/during.js
index dd9ba997a..2f91dd5a8 100644
--- a/lib/during.js
+++ b/lib/during.js
@@ -14,11 +14,10 @@ import wrapAsync from './internal/wrapAsync';
  * @method
  * @see [async.whilst]{@link module:ControlFlow.whilst}
  * @category Control Flow
- * @param {Function} test - asynchronous truth test to perform before each
+ * @param {AsyncFunction} test - asynchronous truth test to perform before each
  * execution of `fn`. Invoked with (callback).
- * @param {Function} fn - A function which is called each time `test` passes.
- * The function is passed a `callback(err)`, which must be called once it has
- * completed with an optional `err` argument. Invoked with (callback).
+ * @param {AsyncFunction} fn - An async function which is called each time
+ * `test` passes. Invoked with (callback).
  * @param {Function} [callback] - A callback which is called after the test
  * function has failed and repeated execution of `fn` has stopped. `callback`
  * will be passed an error, if one occured, otherwise `null`.
diff --git a/lib/eachLimit.js b/lib/eachLimit.js
index c3bc595d0..462e329ee 100644
--- a/lib/eachLimit.js
+++ b/lib/eachLimit.js
@@ -14,12 +14,11 @@ import wrapAsync from './internal/wrapAsync';
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
  * @param {number} limit - The maximum number of async operations at a time.
- * @param {Function} iteratee - A function to apply to each item in `coll`. The
- * iteratee is passed a `callback(err)` which must be called once it has
- * completed. If no error has occurred, the `callback` should be run without
- * arguments or with an explicit `null` argument. The array index is not passed
- * to the iteratee. Invoked with (item, callback). If you need the index, use
- * `eachOfLimit`.
+ * @param {AsyncFunction} iteratee - An async function to apply to each item in
+ * `coll`.
+ * The array index is not passed to the iteratee.
+ * If you need the index, use `eachOfLimit`.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called when all
  * `iteratee` functions have finished, or an error occurs. Invoked with (err).
  */
diff --git a/lib/eachOf.js b/lib/eachOf.js
index 1cfa171dc..9ab3eb6d5 100644
--- a/lib/eachOf.js
+++ b/lib/eachOf.js
@@ -46,12 +46,10 @@ var eachOfGeneric = doLimit(eachOfLimit, Infinity);
  * @category Collection
  * @see [async.each]{@link module:Collections.each}
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A function to apply to each
- * item in `coll`. The `key` is the item's key, or index in the case of an
- * array. The iteratee is passed a `callback(err)` which must be called once it
- * has completed. If no error has occurred, the callback should be run without
- * arguments or with an explicit `null` argument. Invoked with
- * (item, key, callback).
+ * @param {AsyncFunction} iteratee - A function to apply to each
+ * item in `coll`.
+ * The `key` is the item's key, or index in the case of an array.
+ * Invoked with (item, key, callback).
  * @param {Function} [callback] - A callback which is called when all
  * `iteratee` functions have finished, or an error occurs. Invoked with (err).
  * @example
diff --git a/lib/eachOfLimit.js b/lib/eachOfLimit.js
index 17dffc11b..1de28efc6 100644
--- a/lib/eachOfLimit.js
+++ b/lib/eachOfLimit.js
@@ -14,12 +14,10 @@ import wrapAsync from './internal/wrapAsync';
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
  * @param {number} limit - The maximum number of async operations at a time.
- * @param {Function} iteratee - A function to apply to each
+ * @param {AsyncFunction} iteratee - An async function to apply to each
  * item in `coll`. The `key` is the item's key, or index in the case of an
- * array. The iteratee is passed a `callback(err)` which must be called once it
- * has completed. If no error has occurred, the callback should be run without
- * arguments or with an explicit `null` argument. Invoked with
- * (item, key, callback).
+ * array.
+ * Invoked with (item, key, callback).
  * @param {Function} [callback] - A callback which is called when all
  * `iteratee` functions have finished, or an error occurs. Invoked with (err).
  */
diff --git a/lib/eachOfSeries.js b/lib/eachOfSeries.js
index 21e816d37..fc1a09724 100644
--- a/lib/eachOfSeries.js
+++ b/lib/eachOfSeries.js
@@ -12,11 +12,9 @@ import doLimit from './internal/doLimit';
  * @alias forEachOfSeries
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A function to apply to each item in `coll`. The
- * `key` is the item's key, or index in the case of an array. The iteratee is
- * passed a `callback(err)` which must be called once it has completed. If no
- * error has occurred, the callback should be run without arguments or with an
- * explicit `null` argument. Invoked with (item, key, callback).
+ * @param {AsyncFunction} iteratee - An async function to apply to each item in
+ * `coll`.
+ * Invoked with (item, key, callback).
  * @param {Function} [callback] - A callback which is called when all `iteratee`
  * functions have finished, or an error occurs. Invoked with (err).
  */
diff --git a/lib/eachSeries.js b/lib/eachSeries.js
index 0839d8ca1..9f8d7defd 100644
--- a/lib/eachSeries.js
+++ b/lib/eachSeries.js
@@ -12,12 +12,11 @@ import doLimit from './internal/doLimit';
  * @alias forEachSeries
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A function to apply to each
- * item in `coll`. The iteratee is passed a `callback(err)` which must be called
- * once it has completed. If no error has occurred, the `callback` should be run
- * without arguments or with an explicit `null` argument. The array index is
- * not passed to the iteratee. Invoked with (item, callback). If you need the
- * index, use `eachOfSeries`.
+ * @param {AsyncFunction} iteratee - An async function to apply to each
+ * item in `coll`.
+ * The array index is not passed to the iteratee.
+ * If you need the index, use `eachOfSeries`.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called when all
  * `iteratee` functions have finished, or an error occurs. Invoked with (err).
  */
diff --git a/lib/ensureAsync.js b/lib/ensureAsync.js
index 8582bbabd..a579efca6 100644
--- a/lib/ensureAsync.js
+++ b/lib/ensureAsync.js
@@ -8,16 +8,17 @@ import { isAsync } from './internal/wrapAsync';
  * no extra deferral is added. This is useful for preventing stack overflows
  * (`RangeError: Maximum call stack size exceeded`) and generally keeping
  * [Zalgo](http://blog.izs.me/post/59142742143/designing-apis-for-asynchrony)
- * contained.
+ * contained. ES2017 `async` functions are returned as-is -- they are immune
+ * to Zalgo's corrupting influences, as they always resolve on a later tick.
  *
  * @name ensureAsync
  * @static
  * @memberOf module:Utils
  * @method
  * @category Util
- * @param {Function} fn - an async function, one that expects a node-style
+ * @param {AsyncFunction} fn - an async function, one that expects a node-style
  * callback as its last argument.
- * @returns {Function} Returns a wrapped function with the exact same call
+ * @returns {AsyncFunction} Returns a wrapped function with the exact same call
  * signature as the function passed in.
  * @example
  *
diff --git a/lib/every.js b/lib/every.js
index b34ad1f93..eb1074807 100644
--- a/lib/every.js
+++ b/lib/every.js
@@ -13,10 +13,10 @@ import notId from './internal/notId';
  * @alias all
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A truth test to apply to each item in the
- * collection in parallel. The iteratee is passed a `callback(err, truthValue)`
- * which must be called with a  boolean argument once it has completed. Invoked
- * with (item, callback).
+ * @param {AsyncFunction} iteratee - An async truth test to apply to each item
+ * in the collection in parallel.
+ * The iteratee must complete with a boolean result value.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called after all the
  * `iteratee` functions have finished. Result will be either `true` or `false`
  * depending on the values of the async tests. Invoked with (err, result).
diff --git a/lib/everyLimit.js b/lib/everyLimit.js
index 4cc709147..89a69fc01 100644
--- a/lib/everyLimit.js
+++ b/lib/everyLimit.js
@@ -14,10 +14,10 @@ import notId from './internal/notId';
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
  * @param {number} limit - The maximum number of async operations at a time.
- * @param {Function} iteratee - A truth test to apply to each item in the
- * collection in parallel. The iteratee is passed a `callback(err, truthValue)`
- * which must be called with a  boolean argument once it has completed. Invoked
- * with (item, callback).
+ * @param {AsyncFunction} iteratee - An async truth test to apply to each item
+ * in the collection in parallel.
+ * The iteratee must complete with a boolean result value.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called after all the
  * `iteratee` functions have finished. Result will be either `true` or `false`
  * depending on the values of the async tests. Invoked with (err, result).
diff --git a/lib/everySeries.js b/lib/everySeries.js
index 743474805..b67368c95 100644
--- a/lib/everySeries.js
+++ b/lib/everySeries.js
@@ -12,10 +12,10 @@ import doLimit from './internal/doLimit';
  * @alias allSeries
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A truth test to apply to each item in the
- * collection in parallel. The iteratee is passed a `callback(err, truthValue)`
- * which must be called with a  boolean argument once it has completed. Invoked
- * with (item, callback).
+ * @param {AsyncFunction} iteratee - An async truth test to apply to each item
+ * in the collection in series.
+ * The iteratee must complete with a boolean result value.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called after all the
  * `iteratee` functions have finished. Result will be either `true` or `false`
  * depending on the values of the async tests. Invoked with (err, result).
diff --git a/lib/forever.js b/lib/forever.js
index 66bc47276..f7be0b257 100644
--- a/lib/forever.js
+++ b/lib/forever.js
@@ -8,16 +8,16 @@ import wrapAsync from './internal/wrapAsync';
  * Calls the asynchronous function `fn` with a callback parameter that allows it
  * to call itself again, in series, indefinitely.
 
- * If an error is passed to the
- * callback then `errback` is called with the error, and execution stops,
- * otherwise it will never be called.
+ * If an error is passed to the callback then `errback` is called with the
+ * error, and execution stops, otherwise it will never be called.
  *
  * @name forever
  * @static
  * @memberOf module:ControlFlow
  * @method
  * @category Control Flow
- * @param {Function} fn - a function to call repeatedly. Invoked with (next).
+ * @param {AsyncFunction} fn - an async function to call repeatedly.
+ * Invoked with (next).
  * @param {Function} [errback] - when `fn` passes an error to it's callback,
  * this function will be called, and execution stops. Invoked with (err).
  * @example
diff --git a/lib/groupBy.js b/lib/groupBy.js
index 31e2c0b75..a2f923ff5 100644
--- a/lib/groupBy.js
+++ b/lib/groupBy.js
@@ -18,10 +18,10 @@ import groupByLimit from './groupByLimit';
  * @method
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A function to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, key)` which must be called once it
- * has completed with an error (which can be `null`) and the `key` to group the
- * value under. Invoked with (value, callback).
+ * @param {AsyncFunction} iteratee - An async function to apply to each item in
+ * `coll`.
+ * The iteratee should complete with a `key` to group the value under.
+ * Invoked with (value, callback).
  * @param {Function} [callback] - A callback which is called when all `iteratee`
  * functions have finished, or an error occurs. Result is an `Object` whoses
  * properties are arrays of values which returned the corresponding key.
diff --git a/lib/groupByLimit.js b/lib/groupByLimit.js
index c14835191..b0a5ef339 100644
--- a/lib/groupByLimit.js
+++ b/lib/groupByLimit.js
@@ -12,10 +12,10 @@ import wrapAsync from './internal/wrapAsync';
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
  * @param {number} limit - The maximum number of async operations at a time.
- * @param {Function} iteratee - A function to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, key)` which must be called once it
- * has completed with an error (which can be `null`) and the `key` to group the
- * value under. Invoked with (value, callback).
+ * @param {AsyncFunction} iteratee - An async function to apply to each item in
+ * `coll`.
+ * The iteratee should complete with a `key` to group the value under.
+ * Invoked with (value, callback).
  * @param {Function} [callback] - A callback which is called when all `iteratee`
  * functions have finished, or an error occurs. Result is an `Object` whoses
  * properties are arrays of values which returned the corresponding key.
diff --git a/lib/groupBySeries.js b/lib/groupBySeries.js
index 5df9a3cbe..91935c378 100644
--- a/lib/groupBySeries.js
+++ b/lib/groupBySeries.js
@@ -12,10 +12,10 @@ import groupByLimit from './groupByLimit';
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
  * @param {number} limit - The maximum number of async operations at a time.
- * @param {Function} iteratee - A function to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, key)` which must be called once it
- * has completed with an error (which can be `null`) and the `key` to group the
- * value under. Invoked with (value, callback).
+ * @param {AsyncFunction} iteratee - An async function to apply to each item in
+ * `coll`.
+ * The iteratee should complete with a `key` to group the value under.
+ * Invoked with (value, callback).
  * @param {Function} [callback] - A callback which is called when all `iteratee`
  * functions have finished, or an error occurs. Result is an `Object` whoses
  * properties are arrays of values which returned the corresponding key.
diff --git a/lib/index.js b/lib/index.js
index 0fbeefca8..f1e8e988c 100644
--- a/lib/index.js
+++ b/lib/index.js
@@ -3,14 +3,18 @@
  * a variable number of parameters, with the final parameter being a callback.
  * (`function (arg1, arg2, ..., callback) {}`)
  * The final callback is of the form `callback(err, results...)`, which must be
- * called once the function is completed.  The callback can be called with a
+ * called once the function is completed.  The callback should be called with a
  * Error as its first argument to signal that an error occurred.
- * Otherwise, it can be called with `null` as the first argument, and any
- * additional `result` arguments that may apply to signal successful completion.
+ * Otherwise, if no error occurred, it should be called with `null` as the first
+ * argument, and any additional `result` arguments that may apply, to signal
+ * successful completion.
  * The callback must be called exactly once, ideally on a later tick of the
  * JavaScript event loop.
  *
- * This type of function is also referred to as a "Node-style async function".
+ * This type of function is also referred to as a "Node-style async function",
+ * or a "continuation passing-style function" (CPS). Most of the methods of this
+ * library are themselves CPS/Node-style async functions, or functions that
+ * return CPS/Node-style async functions.
  *
  * Wherever we accept a Node-style async function, we also directly accept an
  * [ES2017 `async` function]{@link https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Statements/async_function}.
diff --git a/lib/log.js b/lib/log.js
index 848661da5..c39e03352 100644
--- a/lib/log.js
+++ b/lib/log.js
@@ -11,8 +11,8 @@ import consoleFunc from './internal/consoleFunc';
  * @memberOf module:Utils
  * @method
  * @category Util
- * @param {Function} function - The function you want to eventually apply all
- * arguments to.
+ * @param {AsyncFunction} function - The function you want to eventually apply
+ * all arguments to.
  * @param {...*} arguments... - Any number of arguments to apply to the function.
  * @example
  *
diff --git a/lib/map.js b/lib/map.js
index 76d60582b..100ab7a1a 100644
--- a/lib/map.js
+++ b/lib/map.js
@@ -24,10 +24,10 @@ import map from './internal/map';
  * @method
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A function to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, transformed)` which must be called
- * once it has completed with an error (which can be `null`) and a
- * transformed item. Invoked with (item, callback).
+ * @param {AsyncFunction} iteratee - An async function to apply to each item in
+ * `coll`.
+ * The iteratee should complete with the transformed item.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called when all `iteratee`
  * functions have finished, or an error occurs. Results is an Array of the
  * transformed items from the `coll`. Invoked with (err, results).
diff --git a/lib/mapLimit.js b/lib/mapLimit.js
index a54922d3b..0a2fc02c4 100644
--- a/lib/mapLimit.js
+++ b/lib/mapLimit.js
@@ -12,10 +12,10 @@ import map from './internal/map';
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
  * @param {number} limit - The maximum number of async operations at a time.
- * @param {Function} iteratee - A function to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, transformed)` which must be called
- * once it has completed with an error (which can be `null`) and a transformed
- * item. Invoked with (item, callback).
+ * @param {AsyncFunction} iteratee - An async function to apply to each item in
+ * `coll`.
+ * The iteratee should complete with the transformed item.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called when all `iteratee`
  * functions have finished, or an error occurs. Results is an array of the
  * transformed items from the `coll`. Invoked with (err, results).
diff --git a/lib/mapSeries.js b/lib/mapSeries.js
index e1f3d0d5d..596c75ec7 100644
--- a/lib/mapSeries.js
+++ b/lib/mapSeries.js
@@ -11,10 +11,10 @@ import doLimit from './internal/doLimit';
  * @see [async.map]{@link module:Collections.map}
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A function to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, transformed)` which must be called
- * once it has completed with an error (which can be `null`) and a
- * transformed item. Invoked with (item, callback).
+ * @param {AsyncFunction} iteratee - An async function to apply to each item in
+ * `coll`.
+ * The iteratee should complete with the transformed item.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called when all `iteratee`
  * functions have finished, or an error occurs. Results is an array of the
  * transformed items from the `coll`. Invoked with (err, results).
diff --git a/lib/mapValues.js b/lib/mapValues.js
index afc43f482..d6a4ad23f 100644
--- a/lib/mapValues.js
+++ b/lib/mapValues.js
@@ -21,10 +21,10 @@ import doLimit from './internal/doLimit';
  * @method
  * @category Collection
  * @param {Object} obj - A collection to iterate over.
- * @param {Function} iteratee - A function to apply to each value and key in
- * `coll`. The iteratee is passed a `callback(err, transformed)` which must be
- * called once it has completed with an error (which can be `null`) and a
- * transformed value. Invoked with (value, key, callback).
+ * @param {AsyncFunction} iteratee - A function to apply to each value and key
+ * in `coll`.
+ * The iteratee should complete with the transformed value as its result.
+ * Invoked with (value, key, callback).
  * @param {Function} [callback] - A callback which is called when all `iteratee`
  * functions have finished, or an error occurs. `result` is a new object consisting
  * of each key from `obj`, with each transformed value on the right-hand side.
diff --git a/lib/mapValuesLimit.js b/lib/mapValuesLimit.js
index 1d5a47a85..c6e020d03 100644
--- a/lib/mapValuesLimit.js
+++ b/lib/mapValuesLimit.js
@@ -16,10 +16,10 @@ import wrapAsync from './internal/wrapAsync';
  * @category Collection
  * @param {Object} obj - A collection to iterate over.
  * @param {number} limit - The maximum number of async operations at a time.
- * @param {Function} iteratee - A function to apply to each value in `obj`.
- * The iteratee is passed a `callback(err, transformed)` which must be called
- * once it has completed with an error (which can be `null`) and a
- * transformed value. Invoked with (value, key, callback).
+ * @param {AsyncFunction} iteratee - A function to apply to each value and key
+ * in `coll`.
+ * The iteratee should complete with the transformed value as its result.
+ * Invoked with (value, key, callback).
  * @param {Function} [callback] - A callback which is called when all `iteratee`
  * functions have finished, or an error occurs. `result` is a new object consisting
  * of each key from `obj`, with each transformed value on the right-hand side.
diff --git a/lib/mapValuesSeries.js b/lib/mapValuesSeries.js
index c1530c239..ab0b8f845 100644
--- a/lib/mapValuesSeries.js
+++ b/lib/mapValuesSeries.js
@@ -11,10 +11,10 @@ import doLimit from './internal/doLimit';
  * @see [async.mapValues]{@link module:Collections.mapValues}
  * @category Collection
  * @param {Object} obj - A collection to iterate over.
- * @param {Function} iteratee - A function to apply to each value in `obj`.
- * The iteratee is passed a `callback(err, transformed)` which must be called
- * once it has completed with an error (which can be `null`) and a
- * transformed value. Invoked with (value, key, callback).
+ * @param {AsyncFunction} iteratee - A function to apply to each value and key
+ * in `coll`.
+ * The iteratee should complete with the transformed value as its result.
+ * Invoked with (value, key, callback).
  * @param {Function} [callback] - A callback which is called when all `iteratee`
  * functions have finished, or an error occurs. `result` is a new object consisting
  * of each key from `obj`, with each transformed value on the right-hand side.
diff --git a/lib/memoize.js b/lib/memoize.js
index d752d999a..de71c33e7 100644
--- a/lib/memoize.js
+++ b/lib/memoize.js
@@ -10,7 +10,7 @@ function has(obj, key) {
 }
 
 /**
- * Caches the results of an `async` function. When creating a hash to store
+ * Caches the results of an async function. When creating a hash to store
  * function results against, the callback is omitted from the hash and an
  * optional hash function can be used.
  *
@@ -28,11 +28,11 @@ function has(obj, key) {
  * @memberOf module:Utils
  * @method
  * @category Util
- * @param {Function} fn - The function to proxy and cache results from.
+ * @param {AsyncFunction} fn - The async function to proxy and cache results from.
  * @param {Function} hasher - An optional function for generating a custom hash
  * for storing results. It has all the arguments applied to it apart from the
  * callback, and must be synchronous.
- * @returns {Function} a memoized version of `fn`
+ * @returns {AsyncFunction} a memoized version of `fn`
  * @example
  *
  * var slow_fn = function(name, callback) {
diff --git a/lib/parallel.js b/lib/parallel.js
index 19d555884..8b6c2ce89 100644
--- a/lib/parallel.js
+++ b/lib/parallel.js
@@ -13,6 +13,7 @@ import parallel from './internal/parallel';
  * any I/O, they will actually be executed in series.  Any synchronous setup
  * sections for each task will happen one after the other.  JavaScript remains
  * single-threaded.
+ *
  * **Hint:** Use [`reflect`]{@link module:Utils.reflect} to continue the
  * execution of other tasks when a task fails.
  *
@@ -26,14 +27,14 @@ import parallel from './internal/parallel';
  * @memberOf module:ControlFlow
  * @method
  * @category Control Flow
- * @param {Array|Iterable|Object} tasks - A collection containing functions to run.
- * Each function is passed a `callback(err, result)` which it must call on
- * completion with an error `err` (which can be `null`) and an optional `result`
- * value.
+ * @param {Array|Iterable|Object} tasks - A collection of
+ * [async functions]{@link AsyncFunction} to run.
+ * Each async function can complete with any number of optional `result` values.
  * @param {Function} [callback] - An optional callback to run once all the
  * functions have completed successfully. This function gets a results array
  * (or object) containing all the result arguments passed to the task callbacks.
  * Invoked with (err, results).
+ *
  * @example
  * async.parallel([
  *     function(callback) {
diff --git a/lib/parallelLimit.js b/lib/parallelLimit.js
index 926fa853a..14e9e5230 100644
--- a/lib/parallelLimit.js
+++ b/lib/parallelLimit.js
@@ -11,10 +11,9 @@ import parallel from './internal/parallel';
  * @method
  * @see [async.parallel]{@link module:ControlFlow.parallel}
  * @category Control Flow
- * @param {Array|Collection} tasks - A collection containing functions to run.
- * Each function is passed a `callback(err, result)` which it must call on
- * completion with an error `err` (which can be `null`) and an optional `result`
- * value.
+ * @param {Array|Iterable|Object} tasks - A collection of
+ * [async functions]{@link AsyncFunction} to run.
+ * Each async function can complete with any number of optional `result` values.
  * @param {number} limit - The maximum number of async operations at a time.
  * @param {Function} [callback] - An optional callback to run once all the
  * functions have completed successfully. This function gets a results array
diff --git a/lib/priorityQueue.js b/lib/priorityQueue.js
index 0af01577c..aff729379 100644
--- a/lib/priorityQueue.js
+++ b/lib/priorityQueue.js
@@ -15,11 +15,10 @@ import queue from './queue';
  * @method
  * @see [async.queue]{@link module:ControlFlow.queue}
  * @category Control Flow
- * @param {Function} worker - An asynchronous function for processing a queued
- * task, which must call its `callback(err)` argument when finished, with an
- * optional `error` as an argument.  If you want to handle errors from an
- * individual task, pass a callback to `q.push()`. Invoked with
- * (task, callback).
+ * @param {AsyncFunction} worker - An async function for processing a queued task.
+ * If you want to handle errors from an individual task, pass a callback to
+ * `q.push()`.
+ * Invoked with (task, callback).
  * @param {number} concurrency - An `integer` for determining how many `worker`
  * functions should be run in parallel.  If omitted, the concurrency defaults to
  * `1`.  If the concurrency is `0`, an error is thrown.
diff --git a/lib/queue.js b/lib/queue.js
index 0f17cd996..906467c07 100644
--- a/lib/queue.js
+++ b/lib/queue.js
@@ -59,11 +59,9 @@ import wrapAsync from './internal/wrapAsync';
  * @memberOf module:ControlFlow
  * @method
  * @category Control Flow
- * @param {Function} worker - An asynchronous function for processing a queued
- * task, which must call its `callback(err)` argument when finished, with an
- * optional `error` as an argument.  If you want to handle errors from an
- * individual task, pass a callback to `q.push()`. Invoked with
- * (task, callback).
+ * @param {AsyncFunction} worker - An async function for processing a queued task.
+ * If you want to handle errors from an individual task, pass a callback to
+ * `q.push()`. Invoked with (task, callback).
  * @param {number} [concurrency=1] - An `integer` for determining how many
  * `worker` functions should be run in parallel.  If omitted, the concurrency
  * defaults to `1`.  If the concurrency is `0`, an error is thrown.
diff --git a/lib/race.js b/lib/race.js
index ee81b37be..9b4d6c380 100644
--- a/lib/race.js
+++ b/lib/race.js
@@ -14,9 +14,8 @@ import wrapAsync from './internal/wrapAsync';
  * @memberOf module:ControlFlow
  * @method
  * @category Control Flow
- * @param {Array} tasks - An array containing functions to run. Each function
- * is passed a `callback(err, result)` which it must call on completion with an
- * error `err` (which can be `null`) and an optional `result` value.
+ * @param {Array} tasks - An array containing [async functions]{@link AsyncFunction}
+ * to run. Each function can complete with an optional `result` value.
  * @param {Function} callback - A callback to run once any of the functions have
  * completed. This function gets an error or result from the first function that
  * completed. Invoked with (err, result).
diff --git a/lib/reduce.js b/lib/reduce.js
index c5ac2921e..0d58c41e2 100644
--- a/lib/reduce.js
+++ b/lib/reduce.js
@@ -23,12 +23,12 @@ import wrapAsync from './internal/wrapAsync';
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
  * @param {*} memo - The initial state of the reduction.
- * @param {Function} iteratee - A function applied to each item in the
- * array to produce the next step in the reduction. The `iteratee` is passed a
- * `callback(err, reduction)` which accepts an optional error as its first
- * argument, and the state of the reduction as the second. If an error is
- * passed to the callback, the reduction is stopped and the main `callback` is
- * immediately called with the error. Invoked with (memo, item, callback).
+ * @param {AsyncFunction} iteratee - A function applied to each item in the
+ * array to produce the next step in the reduction.
+ * The `iteratee` should complete with the next state of the reduction.
+ * If the iteratee complete with an error, the reduction is stopped and the
+ * main `callback` is immediately called with the error.
+ * Invoked with (memo, item, callback).
  * @param {Function} [callback] - A callback which is called after all the
  * `iteratee` functions have finished. Result is the reduced value. Invoked with
  * (err, result).
diff --git a/lib/reduceRight.js b/lib/reduceRight.js
index 844c94f93..ca5aa7fb0 100644
--- a/lib/reduceRight.js
+++ b/lib/reduceRight.js
@@ -14,12 +14,12 @@ var slice = Array.prototype.slice;
  * @category Collection
  * @param {Array} array - A collection to iterate over.
  * @param {*} memo - The initial state of the reduction.
- * @param {Function} iteratee - A function applied to each item in the
- * array to produce the next step in the reduction. The `iteratee` is passed a
- * `callback(err, reduction)` which accepts an optional error as its first
- * argument, and the state of the reduction as the second. If an error is
- * passed to the callback, the reduction is stopped and the main `callback` is
- * immediately called with the error. Invoked with (memo, item, callback).
+ * @param {AsyncFunction} iteratee - A function applied to each item in the
+ * array to produce the next step in the reduction.
+ * The `iteratee` should complete with the next state of the reduction.
+ * If the iteratee complete with an error, the reduction is stopped and the
+ * main `callback` is immediately called with the error.
+ * Invoked with (memo, item, callback).
  * @param {Function} [callback] - A callback which is called after all the
  * `iteratee` functions have finished. Result is the reduced value. Invoked with
  * (err, result).
diff --git a/lib/reflect.js b/lib/reflect.js
index 0dbd397a6..9e0613b48 100644
--- a/lib/reflect.js
+++ b/lib/reflect.js
@@ -3,17 +3,17 @@ import rest from './internal/rest';
 import wrapAsync from './internal/wrapAsync';
 
 /**
- * Wraps the function in another function that always returns data even when it
- * errors.
+ * Wraps the async function in another function that always completes with a
+ * result object, even when it errors.
  *
- * The object returned has either the property `error` or `value`.
+ * The result object has either the property `error` or `value`.
  *
  * @name reflect
  * @static
  * @memberOf module:Utils
  * @method
  * @category Util
- * @param {Function} fn - The function you want to wrap
+ * @param {AsyncFunction} fn - The async function you want to wrap
  * @returns {Function} - A function that always passes null to it's callback as
  * the error. The second argument to the callback will be an `object` with
  * either an `error` or a `value` property.
diff --git a/lib/reflectAll.js b/lib/reflectAll.js
index dbeba8d81..0774b9432 100644
--- a/lib/reflectAll.js
+++ b/lib/reflectAll.js
@@ -4,7 +4,7 @@ import _arrayMap from 'lodash/_arrayMap';
 import forOwn from 'lodash/_baseForOwn';
 
 /**
- * A helper function that wraps an array or an object of functions with reflect.
+ * A helper function that wraps an array or an object of functions with `reflect`.
  *
  * @name reflectAll
  * @static
@@ -12,8 +12,9 @@ import forOwn from 'lodash/_baseForOwn';
  * @method
  * @see [async.reflect]{@link module:Utils.reflect}
  * @category Util
- * @param {Array} tasks - The array of functions to wrap in `async.reflect`.
- * @returns {Array} Returns an array of functions, each function wrapped in
+ * @param {Array|Object|Iterable} tasks - The collection of
+ * [async functions]{@link AsyncFunction} to wrap in `async.reflect`.
+ * @returns {Array} Returns an array of async functions, each wrapped in
  * `async.reflect`
  * @example
  *
diff --git a/lib/reject.js b/lib/reject.js
index 0ddbaf0ac..95a627036 100644
--- a/lib/reject.js
+++ b/lib/reject.js
@@ -11,9 +11,10 @@ import doParallel from './internal/doParallel';
  * @see [async.filter]{@link module:Collections.filter}
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A truth test to apply to each item in `coll`.
- * The `iteratee` is passed a `callback(err, truthValue)`, which must be called
- * with a boolean argument once it has completed. Invoked with (item, callback).
+ * @param {Function} iteratee - An async truth test to apply to each item in
+ * `coll`.
+ * The should complete with a boolean value as its `result`.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called after all the
  * `iteratee` functions have finished. Invoked with (err, results).
  * @example
diff --git a/lib/rejectLimit.js b/lib/rejectLimit.js
index 977bc4c83..814781138 100644
--- a/lib/rejectLimit.js
+++ b/lib/rejectLimit.js
@@ -13,9 +13,10 @@ import doParallelLimit from './internal/doParallelLimit';
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
  * @param {number} limit - The maximum number of async operations at a time.
- * @param {Function} iteratee - A truth test to apply to each item in `coll`.
- * The `iteratee` is passed a `callback(err, truthValue)`, which must be called
- * with a boolean argument once it has completed. Invoked with (item, callback).
+ * @param {Function} iteratee - An async truth test to apply to each item in
+ * `coll`.
+ * The should complete with a boolean value as its `result`.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called after all the
  * `iteratee` functions have finished. Invoked with (err, results).
  */
diff --git a/lib/rejectSeries.js b/lib/rejectSeries.js
index 0bb925e97..7eba2f736 100644
--- a/lib/rejectSeries.js
+++ b/lib/rejectSeries.js
@@ -11,9 +11,10 @@ import doLimit from './internal/doLimit';
  * @see [async.reject]{@link module:Collections.reject}
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A truth test to apply to each item in `coll`.
- * The `iteratee` is passed a `callback(err, truthValue)`, which must be called
- * with a boolean argument once it has completed. Invoked with (item, callback).
+ * @param {Function} iteratee - An async truth test to apply to each item in
+ * `coll`.
+ * The should complete with a boolean value as its `result`.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called after all the
  * `iteratee` functions have finished. Invoked with (err, results).
  */
diff --git a/lib/retry.js b/lib/retry.js
index e2790160e..bd60644ce 100644
--- a/lib/retry.js
+++ b/lib/retry.js
@@ -13,6 +13,7 @@ import wrapAsync from './internal/wrapAsync';
  * @memberOf module:ControlFlow
  * @method
  * @category Control Flow
+ * @see [async.retryable]{@link module:ControlFlow.retryable}
  * @param {Object|number} [opts = {times: 5, interval: 0}| 5] - Can be either an
  * object with `times` and `interval` or a number.
  * * `times` - The number of attempts to make before giving up.  The default
@@ -27,16 +28,13 @@ import wrapAsync from './internal/wrapAsync';
  *   Invoked with (err).
  * * If `opts` is a number, the number specifies the number of times to retry,
  *   with the default interval of `0`.
- * @param {Function} task - A function which receives two arguments: (1) a
- * `callback(err, result)` which must be called when finished, passing `err`
- * (which can be `null`) and the `result` of the function's execution, and (2)
- * a `results` object, containing the results of the previously executed
- * functions (if nested inside another control flow). Invoked with
- * (callback, results).
+ * @param {AsyncFunction} task - An async function to retry.
+ * Invoked with (callback).
  * @param {Function} [callback] - An optional callback which is called when the
  * task has succeeded, or after the final failed attempt. It receives the `err`
  * and `result` arguments of the last attempt at completing the `task`. Invoked
  * with (err, results).
+ *
  * @example
  *
  * // The `retry` function can be used as a stand-alone control flow by passing
@@ -82,7 +80,7 @@ import wrapAsync from './internal/wrapAsync';
  * // individual methods that are not as reliable, like this:
  * async.auto({
  *     users: api.getUsers.bind(api),
- *     payments: async.retry(3, api.getPayments.bind(api))
+ *     payments: async.retryable(3, api.getPayments.bind(api))
  * }, function(err, results) {
  *     // do something with the results
  * });
diff --git a/lib/retryable.js b/lib/retryable.js
index 6fba8e234..57410317a 100644
--- a/lib/retryable.js
+++ b/lib/retryable.js
@@ -3,8 +3,9 @@ import initialParams from './internal/initialParams';
 import wrapAsync from './internal/wrapAsync';
 
 /**
- * A close relative of [`retry`]{@link module:ControlFlow.retry}.  This method wraps a task and makes it
- * retryable, rather than immediately calling it with retries.
+ * A close relative of [`retry`]{@link module:ControlFlow.retry}.  This method
+ * wraps a task and makes it retryable, rather than immediately calling it
+ * with retries.
  *
  * @name retryable
  * @static
@@ -14,9 +15,12 @@ import wrapAsync from './internal/wrapAsync';
  * @category Control Flow
  * @param {Object|number} [opts = {times: 5, interval: 0}| 5] - optional
  * options, exactly the same as from `retry`
- * @param {Function} task - the asynchronous function to wrap
- * @returns {Functions} The wrapped function, which when invoked, will retry on
- * an error, based on the parameters specified in `opts`.
+ * @param {AsyncFunction} task - the asynchronous function to wrap.
+ * This function will be passed any arguments passed to the returned wrapper.
+ * Invoked with (...args, callback).
+ * @returns {AsyncFunction} The wrapped function, which when invoked, will
+ * retry on an error, based on the parameters specified in `opts`.
+ * This function will accept the same parameters as `task`.
  * @example
  *
  * async.auto({
diff --git a/lib/seq.js b/lib/seq.js
index 9a3584718..4fceceb60 100644
--- a/lib/seq.js
+++ b/lib/seq.js
@@ -17,7 +17,7 @@ import arrayMap from 'lodash/_arrayMap';
  * @method
  * @see [async.compose]{@link module:ControlFlow.compose}
  * @category Control Flow
- * @param {...Function} functions - the asynchronous functions to compose
+ * @param {...AsyncFunction} functions - the asynchronous functions to compose
  * @returns {Function} a function that composes the `functions` in order
  * @example
  *
diff --git a/lib/series.js b/lib/series.js
index 7955cf251..eef153411 100644
--- a/lib/series.js
+++ b/lib/series.js
@@ -27,9 +27,9 @@ import eachOfSeries from './eachOfSeries';
  * @memberOf module:ControlFlow
  * @method
  * @category Control Flow
- * @param {Array|Iterable|Object} tasks - A collection containing functions to run, each
- * function is passed a `callback(err, result)` it must call on completion with
- * an error `err` (which can be `null`) and an optional `result` value.
+ * @param {Array|Iterable|Object} tasks - A collection containing
+ * [async functions]{@link AsyncFunction} to run in series.
+ * Each function can complete with any number of optional `result` values.
  * @param {Function} [callback] - An optional callback to run once all the
  * functions have completed. This function gets a results array (or object)
  * containing all the result arguments passed to the `task` callbacks. Invoked
diff --git a/lib/someLimit.js b/lib/someLimit.js
index bf4c601cb..161c3cfe2 100644
--- a/lib/someLimit.js
+++ b/lib/someLimit.js
@@ -14,10 +14,10 @@ import identity from 'lodash/identity';
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
  * @param {number} limit - The maximum number of async operations at a time.
- * @param {Function} iteratee - A truth test to apply to each item in the array
- * in parallel. The iteratee is passed a `callback(err, truthValue)` which must
- * be called with a boolean argument once it has completed. Invoked with
- * (item, callback).
+ * @param {AsyncFunction} iteratee - An async truth test to apply to each item
+ * in the collections in parallel.
+ * The iteratee should complete with a boolean `result` value.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called as soon as any
  * iteratee returns `true`, or after all the iteratee functions have finished.
  * Result will be either `true` or `false` depending on the values of the async
diff --git a/lib/someSeries.js b/lib/someSeries.js
index 8357a8b16..8e278deb7 100644
--- a/lib/someSeries.js
+++ b/lib/someSeries.js
@@ -12,10 +12,10 @@ import doLimit from './internal/doLimit';
  * @alias anySeries
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A truth test to apply to each item in the array
- * in parallel. The iteratee is passed a `callback(err, truthValue)` which must
- * be called with a boolean argument once it has completed. Invoked with
- * (item, callback).
+ * @param {AsyncFunction} iteratee - An async truth test to apply to each item
+ * in the collections in series.
+ * The iteratee should complete with a boolean `result` value.
+ * Invoked with (item, callback).
  * @param {Function} [callback] - A callback which is called as soon as any
  * iteratee returns `true`, or after all the iteratee functions have finished.
  * Result will be either `true` or `false` depending on the values of the async
diff --git a/lib/sortBy.js b/lib/sortBy.js
index 812a39ef3..399debd23 100644
--- a/lib/sortBy.js
+++ b/lib/sortBy.js
@@ -14,10 +14,11 @@ import wrapAsync from './internal/wrapAsync';
  * @method
  * @category Collection
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
- * @param {Function} iteratee - A function to apply to each item in `coll`.
- * The iteratee is passed a `callback(err, sortValue)` which must be called once
- * it has completed with an error (which can be `null`) and a value to use as
- * the sort criteria. Invoked with (item, callback).
+ * @param {AsyncFunction} iteratee - An async function to apply to each item in
+ * `coll`.
+ * The iteratee should complete with a value to use as the sort criteria as
+ * its `result`.
+ * Invoked with (item, callback).
  * @param {Function} callback - A callback which is called after all the
  * `iteratee` functions have finished, or an error occurs. Results is the items
  * from the original `coll` sorted by the values returned by the `iteratee`
diff --git a/lib/timeout.js b/lib/timeout.js
index ad050e01a..475b20889 100644
--- a/lib/timeout.js
+++ b/lib/timeout.js
@@ -11,14 +11,13 @@ import wrapAsync from './internal/wrapAsync';
  * @memberOf module:Utils
  * @method
  * @category Util
- * @param {Function} asyncFn - The asynchronous function you want to set the
- * time limit.
+ * @param {AsyncFunction} asyncFn - The async function to limit in time.
  * @param {number} milliseconds - The specified time limit.
  * @param {*} [info] - Any variable you want attached (`string`, `object`, etc)
  * to timeout Error for more information..
- * @returns {Function} Returns a wrapped function that can be used with any of
- * the control flow functions. Invoke this function with the same
- * parameters as you would `asyncFunc`.
+ * @returns {AsyncFunction} Returns a wrapped function that can be used with any
+ * of the control flow functions.
+ * Invoke this function with the same parameters as you would `asyncFunc`.
  * @example
  *
  * function myFunction(foo, callback) {
diff --git a/lib/times.js b/lib/times.js
index bdd2e6b34..ebd336c4c 100644
--- a/lib/times.js
+++ b/lib/times.js
@@ -12,8 +12,8 @@ import doLimit from './internal/doLimit';
  * @see [async.map]{@link module:Collections.map}
  * @category Control Flow
  * @param {number} n - The number of times to run the function.
- * @param {Function} iteratee - The function to call `n` times. Invoked with the
- * iteration index and a callback (n, next).
+ * @param {AsyncFunction} iteratee - The async function to call `n` times.
+ * Invoked with the iteration index and a callback: (n, next).
  * @param {Function} callback - see {@link module:Collections.map}.
  * @example
  *
diff --git a/lib/timesLimit.js b/lib/timesLimit.js
index 7ba91d69c..22be265a1 100644
--- a/lib/timesLimit.js
+++ b/lib/timesLimit.js
@@ -14,8 +14,8 @@ import wrapAsync from './internal/wrapAsync';
  * @category Control Flow
  * @param {number} count - The number of times to run the function.
  * @param {number} limit - The maximum number of async operations at a time.
- * @param {Function} iteratee - The function to call `n` times. Invoked with the
- * iteration index and a callback (n, next).
+ * @param {AsyncFunction} iteratee - The async function to call `n` times.
+ * Invoked with the iteration index and a callback: (n, next).
  * @param {Function} callback - see [async.map]{@link module:Collections.map}.
  */
 export default function timeLimit(count, limit, iteratee, callback) {
diff --git a/lib/timesSeries.js b/lib/timesSeries.js
index 672428d18..17ec0ca85 100644
--- a/lib/timesSeries.js
+++ b/lib/timesSeries.js
@@ -11,8 +11,8 @@ import doLimit from './internal/doLimit';
  * @see [async.times]{@link module:ControlFlow.times}
  * @category Control Flow
  * @param {number} n - The number of times to run the function.
- * @param {Function} iteratee - The function to call `n` times. Invoked with the
- * iteration index and a callback (n, next).
+ * @param {AsyncFunction} iteratee - The async function to call `n` times.
+ * Invoked with the iteration index and a callback: (n, next).
  * @param {Function} callback - see {@link module:Collections.map}.
  */
 export default doLimit(timesLimit, 1);
diff --git a/lib/transform.js b/lib/transform.js
index d3c1d6a03..ef254a136 100644
--- a/lib/transform.js
+++ b/lib/transform.js
@@ -18,11 +18,8 @@ import wrapAsync from './internal/wrapAsync';
  * @param {Array|Iterable|Object} coll - A collection to iterate over.
  * @param {*} [accumulator] - The initial state of the transform.  If omitted,
  * it will default to an empty Object or Array, depending on the type of `coll`
- * @param {Function} iteratee - A function applied to each item in the
- * collection that potentially modifies the accumulator. The `iteratee` is
- * passed a `callback(err)` which accepts an optional error as its first
- * argument. If an error is passed to the callback, the transform is stopped
- * and the main `callback` is immediately called with the error.
+ * @param {AsyncFunction} iteratee - A function applied to each item in the
+ * collection that potentially modifies the accumulator.
  * Invoked with (accumulator, item, key, callback).
  * @param {Function} [callback] - A callback which is called after all the
  * `iteratee` functions have finished. Result is the transformed accumulator.
diff --git a/lib/unmemoize.js b/lib/unmemoize.js
index 4b2db4dc8..d89075f5d 100644
--- a/lib/unmemoize.js
+++ b/lib/unmemoize.js
@@ -8,8 +8,8 @@
  * @method
  * @see [async.memoize]{@link module:Utils.memoize}
  * @category Util
- * @param {Function} fn - the memoized function
- * @returns {Function} a function that calls the original unmemoized function
+ * @param {AsyncFunction} fn - the memoized function
+ * @returns {AsyncFunction} a function that calls the original unmemoized function
  */
 export default  function unmemoize(fn) {
     return function () {
diff --git a/lib/whilst.js b/lib/whilst.js
index 8135af7d9..dc56a8a24 100644
--- a/lib/whilst.js
+++ b/lib/whilst.js
@@ -15,9 +15,8 @@ import wrapAsync from './internal/wrapAsync';
  * @category Control Flow
  * @param {Function} test - synchronous truth test to perform before each
  * execution of `iteratee`. Invoked with ().
- * @param {Function} iteratee - A function which is called each time `test` passes.
- * The function is passed a `callback(err)`, which must be called once it has
- * completed with an optional `err` argument. Invoked with (callback).
+ * @param {AsyncFunction} fn - An async function which is called each time
+ * `test` passes. Invoked with (callback).
  * @param {Function} [callback] - A callback which is called after the test
  * function has failed and repeated execution of `iteratee` has stopped. `callback`
  * will be passed an error and any arguments passed to the final `iteratee`'s