diff --git a/CHANGES.rst b/CHANGES.rst
index 5293cd874..386a759ab 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -1,3 +1,12 @@
+3.1.0 (unreleased)
+------------------
+
+The ASDF Standard is at v1.6.0
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+- Cleanup ``asdf.util`` including deprecating: ``human_list``
+  ``resolve_name`` ``minversion`` and ``iter_subclasses`` [#1688]
+
 3.0.1 (2023-10-30)
 ------------------
 
diff --git a/asdf/_block/external.py b/asdf/_block/external.py
index 6e5f41620..734e9a773 100644
--- a/asdf/_block/external.py
+++ b/asdf/_block/external.py
@@ -40,7 +40,7 @@ def load(self, base_uri, uri, memmap=False, validate_checksums=False):
             ) as af:
                 blk = af._blocks.blocks[0]
                 if memmap and blk.header["compression"] == b"\0\0\0\0":
-                    parsed_url = util.patched_urllib_parse.urlparse(resolved_uri)
+                    parsed_url = util._patched_urllib_parse.urlparse(resolved_uri)
                     if parsed_url.scheme == "file":
                         # deal with leading slash for windows file://
                         filename = urllib.request.url2pathname(parsed_url.path)
@@ -58,7 +58,7 @@ def clear(self):
 
 def relative_uri_for_index(uri, index):
     # get the os-native separated path for this uri
-    path = util.patched_urllib_parse.urlparse(uri).path
+    path = util._patched_urllib_parse.urlparse(uri).path
     dirname, filename = os.path.split(path)
     filename = os.path.splitext(filename)[0] + f"{index:04d}.asdf"
     return filename
diff --git a/asdf/_block/io.py b/asdf/_block/io.py
index e0afa7d23..ce93f9a11 100644
--- a/asdf/_block/io.py
+++ b/asdf/_block/io.py
@@ -15,7 +15,7 @@
 
 from .exceptions import BlockIndexError
 
-BLOCK_HEADER = util.BinaryStruct(
+BLOCK_HEADER = util._BinaryStruct(
     [
         ("flags", "I"),
         ("compression", "4s"),
@@ -83,7 +83,7 @@ def read_block_header(fd, offset=None):
     -------
     header : dict
         Dictionary containing the read ASDF header as parsed by the
-        `BLOCK_HEADER` `asdf.util.BinaryStruct`.
+        `BLOCK_HEADER` `asdf.util._BinaryStruct`.
 
     Raises
     ------
diff --git a/asdf/_tests/test_deprecated.py b/asdf/_tests/test_deprecated.py
index fa5ee6016..62ecd050b 100644
--- a/asdf/_tests/test_deprecated.py
+++ b/asdf/_tests/test_deprecated.py
@@ -2,6 +2,7 @@
 
 import pytest
 
+import asdf
 from asdf.exceptions import AsdfDeprecationWarning
 
 
@@ -15,3 +16,23 @@ def test_asdf_stream_deprecation():
 def test_asdf_asdf_SerializationContext_import_deprecation():
     with pytest.warns(AsdfDeprecationWarning, match="importing SerializationContext from asdf.asdf"):
         from asdf.asdf import SerializationContext  # noqa: F401
+
+
+def test_asdf_util_human_list_deprecation():
+    with pytest.warns(AsdfDeprecationWarning, match="asdf.util.human_list is deprecated"):
+        asdf.util.human_list("a")
+
+
+def test_asdf_util_resolve_name_deprecation():
+    with pytest.warns(AsdfDeprecationWarning, match="asdf.util.resolve_name is deprecated"):
+        asdf.util.resolve_name("asdf.AsdfFile")
+
+
+def test_asdf_util_minversion_deprecation():
+    with pytest.warns(AsdfDeprecationWarning, match="asdf.util.minversion is deprecated"):
+        asdf.util.minversion("yaml", "3.1")
+
+
+def test_asdf_util_iter_subclasses_deprecation():
+    with pytest.warns(AsdfDeprecationWarning, match="asdf.util.iter_subclasses is deprecated"):
+        list(asdf.util.iter_subclasses(asdf.AsdfFile))
diff --git a/asdf/_tests/test_util.py b/asdf/_tests/test_util.py
index e305bb25c..a0830b61d 100644
--- a/asdf/_tests/test_util.py
+++ b/asdf/_tests/test_util.py
@@ -1,8 +1,10 @@
 import io
+import warnings
 
 import pytest
 
 from asdf import generic_io, util
+from asdf.exceptions import AsdfDeprecationWarning
 
 
 def test_is_primitive():
@@ -35,12 +37,12 @@ def test_get_class_name():
 
 
 def test_patched_urllib_parse():
-    assert "asdf" in util.patched_urllib_parse.uses_relative
-    assert "asdf" in util.patched_urllib_parse.uses_netloc
+    assert "asdf" in util._patched_urllib_parse.uses_relative
+    assert "asdf" in util._patched_urllib_parse.uses_netloc
 
     import urllib.parse
 
-    assert urllib.parse is not util.patched_urllib_parse
+    assert urllib.parse is not util._patched_urllib_parse
     assert "asdf" not in urllib.parse.uses_relative
     assert "asdf" not in urllib.parse.uses_netloc
 
@@ -103,12 +105,14 @@ def test_minversion():
 
     good_versions = ["1.16", "1.16.1", "1.16.0.dev", "1.16dev"]
     bad_versions = ["100000", "100000.2rc1"]
-    for version in good_versions:
-        assert util.minversion(np, version)
-        assert util.minversion("numpy", version)
-    for version in bad_versions:
-        assert not util.minversion(np, version)
-        assert not util.minversion("numpy", version)
-
-    assert util.minversion(yaml, "3.1")
-    assert util.minversion("yaml", "3.1")
+    with warnings.catch_warnings():
+        warnings.filterwarnings("ignore", "asdf.util.minversion", AsdfDeprecationWarning)
+        for version in good_versions:
+            assert util.minversion(np, version)
+            assert util.minversion("numpy", version)
+        for version in bad_versions:
+            assert not util.minversion(np, version)
+            assert not util.minversion("numpy", version)
+
+        assert util.minversion(yaml, "3.1")
+        assert util.minversion("yaml", "3.1")
diff --git a/asdf/commands/diff.py b/asdf/commands/diff.py
index 7c682fa74..711ad9c9c 100644
--- a/asdf/commands/diff.py
+++ b/asdf/commands/diff.py
@@ -33,7 +33,6 @@
 import asdf
 from asdf.extension._serialization_context import BlockAccess
 from asdf.tagged import Tagged
-from asdf.util import human_list
 
 from .main import Command
 
@@ -256,6 +255,34 @@ def _load_array(asdf_file, array_dict):
     return conv.from_yaml_tree(array_dict, array_dict._tag, sctx)
 
 
+def _human_list(line, separator="and"):
+    """
+    Formats a list for human readability.
+
+    Parameters
+    ----------
+    line : sequence
+        A sequence of strings
+
+    separator : string, optional
+        The word to use between the last two entries.  Default:
+        ``"and"``.
+
+    Returns
+    -------
+    formatted_list : string
+
+    Examples
+    --------
+    >>> _human_list(["vanilla", "strawberry", "chocolate"], "or")
+    'vanilla, strawberry or chocolate'
+    """
+    if len(line) == 1:
+        return line[0]
+
+    return ", ".join(line[:-1]) + " " + separator + " " + line[-1]
+
+
 def compare_ndarrays(diff_ctx, array0, array1, keys):
     """Compares two ndarray objects"""
     if isinstance(array0, list):
@@ -278,7 +305,7 @@ def compare_ndarrays(diff_ctx, array0, array1, keys):
         differences.append("contents")
 
     if differences:
-        msg = f"ndarrays differ by {human_list(differences)}"
+        msg = f"ndarrays differ by {_human_list(differences)}"
         print_in_tree(diff_ctx, keys, msg, False, ignore_lwl=True)
         print_in_tree(diff_ctx, keys, msg, True, ignore_lwl=True)
 
diff --git a/asdf/commands/main.py b/asdf/commands/main.py
index 057181eb4..d927f55e8 100644
--- a/asdf/commands/main.py
+++ b/asdf/commands/main.py
@@ -37,7 +37,7 @@ def help_(args):
     help_parser = subparsers.add_parser("help", help="Display usage information")
     help_parser.set_defaults(func=help_)
 
-    commands = {x.__name__: x for x in util.iter_subclasses(Command)}
+    commands = {x.__name__: x for x in util._iter_subclasses(Command)}
 
     for command in command_order:
         commands[str(command)].setup_arguments(subparsers)
diff --git a/asdf/core/_converters/complex.py b/asdf/core/_converters/complex.py
index acf95c98d..52e2f6daa 100644
--- a/asdf/core/_converters/complex.py
+++ b/asdf/core/_converters/complex.py
@@ -14,7 +14,7 @@
 class ComplexConverter(Converter):
     tags = ["tag:stsci.edu:asdf/core/complex-1.0.0"]
 
-    types = [*list(util.iter_subclasses(np.complexfloating)), complex]
+    types = [*list(util._iter_subclasses(np.complexfloating)), complex]
 
     def to_yaml_tree(self, obj, tag, ctx):
         return str(obj)
diff --git a/asdf/generic_io.py b/asdf/generic_io.py
index f4cb42d9d..1ebe660fc 100644
--- a/asdf/generic_io.py
+++ b/asdf/generic_io.py
@@ -22,7 +22,7 @@
 from . import util
 from .exceptions import DelimiterNotFoundError
 from .extern import atomicfile
-from .util import patched_urllib_parse
+from .util import _patched_urllib_parse
 
 __all__ = ["get_file", "get_uri", "resolve_uri", "relative_uri"]
 
@@ -69,8 +69,8 @@ def resolve_uri(base, uri):
     """
     if base is None:
         base = ""
-    resolved = patched_urllib_parse.urljoin(base, uri)
-    parsed = patched_urllib_parse.urlparse(resolved)
+    resolved = _patched_urllib_parse.urljoin(base, uri)
+    parsed = _patched_urllib_parse.urlparse(resolved)
     if parsed.path != "" and not parsed.path.startswith("/"):
         msg = "Resolved to relative URL"
         raise ValueError(msg)
@@ -81,8 +81,8 @@ def relative_uri(source, target):
     """
     Make a relative URI from source to target.
     """
-    su = patched_urllib_parse.urlparse(source)
-    tu = patched_urllib_parse.urlparse(target)
+    su = _patched_urllib_parse.urlparse(source)
+    tu = _patched_urllib_parse.urlparse(target)
     extra = list(tu[3:])
     relative = None
     if tu[0] == "" and tu[1] == "":
@@ -98,7 +98,7 @@ def relative_uri(source, target):
     if relative == ".":
         relative = ""
 
-    return patched_urllib_parse.urlunparse(["", "", relative, *extra])
+    return _patched_urllib_parse.urlunparse(["", "", relative, *extra])
 
 
 class _TruncatedReader:
@@ -187,7 +187,7 @@ def read(self, nbytes=None):
         return content
 
 
-class GenericFile(metaclass=util.InheritDocstrings):
+class GenericFile(metaclass=util._InheritDocstrings):
     """
     Base class for an abstraction layer around a number of different
     file-like types.  Each of its subclasses handles a particular kind
@@ -1094,7 +1094,7 @@ def get_file(init, mode="r", uri=None, close=False):
         return GenericWrapper(init)
 
     if isinstance(init, (str, pathlib.Path)):
-        parsed = patched_urllib_parse.urlparse(str(init))
+        parsed = _patched_urllib_parse.urlparse(str(init))
         if parsed.scheme in ["http", "https"]:
             if "w" in mode:
                 msg = "HTTP connections can not be opened for writing"
diff --git a/asdf/reference.py b/asdf/reference.py
index 91f835efd..6d4250c5c 100644
--- a/asdf/reference.py
+++ b/asdf/reference.py
@@ -12,7 +12,7 @@
 import numpy as np
 
 from . import generic_io, treeutil, util
-from .util import patched_urllib_parse
+from .util import _patched_urllib_parse
 
 __all__ = ["resolve_fragment", "Reference", "find_references", "resolve_references", "make_reference"]
 
@@ -22,7 +22,7 @@ def resolve_fragment(tree, pointer):
     Resolve a JSON Pointer within the tree.
     """
     pointer = pointer.lstrip("/")
-    parts = patched_urllib_parse.unquote(pointer).split("/") if pointer else []
+    parts = _patched_urllib_parse.unquote(pointer).split("/") if pointer else []
 
     for part in parts:
         part_ = part.replace("~1", "/").replace("~0", "~")
@@ -57,7 +57,7 @@ def _get_target(self, **kwargs):
                 base_uri = self._asdffile().uri
             uri = generic_io.resolve_uri(base_uri, self._uri)
             asdffile = self._asdffile().open_external(uri, **kwargs)
-            parts = patched_urllib_parse.urlparse(self._uri)
+            parts = _patched_urllib_parse.urlparse(self._uri)
             fragment = parts.fragment
             self._target = resolve_fragment(asdffile.tree, fragment)
         return self._target
diff --git a/asdf/schema.py b/asdf/schema.py
index 477fc1000..f0daefaca 100644
--- a/asdf/schema.py
+++ b/asdf/schema.py
@@ -17,7 +17,7 @@
 from . import constants, generic_io, reference, tagged, treeutil, util, versioning, yamlutil
 from .config import get_config
 from .exceptions import AsdfDeprecationWarning, AsdfWarning
-from .util import patched_urllib_parse
+from .util import _patched_urllib_parse
 
 YAML_SCHEMA_METASCHEMA_ID = "http://stsci.edu/schemas/yaml-schema/draft-01"
 
@@ -381,7 +381,7 @@ def get_schema(url):
 
     # Supplying our own implementation of urljoin_cache
     # allows asdf:// URIs to be resolved correctly.
-    urljoin_cache = lru_cache(1024)(patched_urllib_parse.urljoin)
+    urljoin_cache = lru_cache(1024)(_patched_urllib_parse.urljoin)
 
     # We set cache_remote=False here because we do the caching of
     # remote schemas here in `load_schema`, so we don't need
diff --git a/asdf/util.py b/asdf/util.py
index 47b26ffef..36cafd3ed 100644
--- a/asdf/util.py
+++ b/asdf/util.py
@@ -5,6 +5,7 @@
 import re
 import struct
 import types
+import warnings
 from functools import lru_cache
 from importlib import metadata
 from urllib.request import pathname2url
@@ -20,21 +21,22 @@
 from packaging.version import Version
 
 from . import constants
+from .exceptions import AsdfDeprecationWarning
 
 # We're importing our own copy of urllib.parse because
 # we need to patch it to support asdf:// URIs, but it'd
 # be irresponsible to do this for all users of a
 # standard library.
 urllib_parse_spec = importlib.util.find_spec("urllib.parse")
-patched_urllib_parse = importlib.util.module_from_spec(urllib_parse_spec)
-urllib_parse_spec.loader.exec_module(patched_urllib_parse)
+_patched_urllib_parse = importlib.util.module_from_spec(urllib_parse_spec)
+urllib_parse_spec.loader.exec_module(_patched_urllib_parse)
 del urllib_parse_spec
 
 # urllib.parse needs to know that it should treat asdf://
 # URIs like http:// URIs for the purposes of joining
 # a relative path to a base URI.
-patched_urllib_parse.uses_relative.append("asdf")
-patched_urllib_parse.uses_netloc.append("asdf")
+_patched_urllib_parse.uses_relative.append("asdf")
+_patched_urllib_parse.uses_netloc.append("asdf")
 
 
 __all__ = [
@@ -49,6 +51,8 @@
     "is_primitive",
     "uri_match",
     "get_class_name",
+    "get_file_type",
+    "FileType",
 ]
 
 
@@ -71,9 +75,10 @@ def human_list(line, separator="and"):
 
     Examples
     --------
-    >>> human_list(["vanilla", "strawberry", "chocolate"], "or")
+    >>> human_list(["vanilla", "strawberry", "chocolate"], "or")  # doctest: +SKIP
     'vanilla, strawberry or chocolate'
     """
+    warnings.warn("asdf.util.human_list is deprecated", AsdfDeprecationWarning)
     if len(line) == 1:
         return line[0]
 
@@ -97,24 +102,32 @@ def get_base_uri(uri):
     """
     For a given URI, return the part without any fragment.
     """
-    parts = patched_urllib_parse.urlparse(uri)
-    return patched_urllib_parse.urlunparse([*list(parts[:5]), ""])
+    parts = _patched_urllib_parse.urlparse(uri)
+    return _patched_urllib_parse.urlunparse([*list(parts[:5]), ""])
 
 
 def filepath_to_url(path):
     """
     For a given local file path, return a file:// url.
     """
-    return patched_urllib_parse.urljoin("file:", pathname2url(path))
+    return _patched_urllib_parse.urljoin("file:", pathname2url(path))
 
 
-def iter_subclasses(cls):
+def _iter_subclasses(cls):
     """
     Returns all subclasses of a class.
     """
     for x in cls.__subclasses__():
         yield x
-        yield from iter_subclasses(x)
+        yield from _iter_subclasses(x)
+
+
+def iter_subclasses(cls):
+    """
+    Returns all subclasses of a class.
+    """
+    warnings.warn("asdf.util.iter_subclasses is deprecated", AsdfDeprecationWarning)
+    yield from _iter_subclasses(cls)
 
 
 def calculate_padding(content_size, pad_blocks, block_size):
@@ -151,7 +164,7 @@ def calculate_padding(content_size, pad_blocks, block_size):
     return max(new_size - content_size, 0)
 
 
-class BinaryStruct:
+class _BinaryStruct:
     """
     A wrapper around the Python stdlib struct module to define a
     binary struct more like a dictionary than a tuple.
@@ -267,7 +280,7 @@ def resolve_name(name):
     Examples
     --------
 
-    >>> resolve_name('asdf.util.resolve_name')
+    >>> resolve_name('asdf.util.resolve_name')  # doctest: +SKIP
     <function resolve_name at 0x...>
 
     Raises
@@ -276,6 +289,8 @@ def resolve_name(name):
         If the module or named object is not found.
     """
 
+    warnings.warn("asdf.util.resolve_name is deprecated, see astropy.utils.resolve_name", AsdfDeprecationWarning)
+
     # Note: On python 2 these must be str objects and not unicode
     parts = [str(part) for part in name.split(".")]
 
@@ -351,6 +366,8 @@ def minversion(module, version, inclusive=True):
         as opposed to strictly greater than (default: `True`).
     """
 
+    warnings.warn("asdf.util.minversion is deprecated, see astropy.utils.minversion", AsdfDeprecationWarning)
+
     if isinstance(module, types.ModuleType):
         module_name = module.__name__
         module_version = getattr(module, "__version__", None)
@@ -358,7 +375,9 @@ def minversion(module, version, inclusive=True):
         module_name = module
         module_version = None
         try:
-            module = resolve_name(module_name)
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", "asdf.util.resolve_name", AsdfDeprecationWarning)
+                module = resolve_name(module_name)
         except ImportError:
             return False
     else:
@@ -382,7 +401,7 @@ def minversion(module, version, inclusive=True):
     return Version(module_version) > Version(version)
 
 
-class InheritDocstrings(type):
+class _InheritDocstrings(type):
     """
     This metaclass makes methods of a class automatically have their
     docstrings filled in from the methods they override in the base
@@ -396,8 +415,8 @@ class InheritDocstrings(type):
 
     For example::
 
-        >>> from asdf.util import InheritDocstrings
-        >>> class A(metaclass=InheritDocstrings):
+        >>> from asdf.util import _InheritDocstrings
+        >>> class A(metaclass=_InheritDocstrings):
         ...     def wiggle(self):
         ...         "Wiggle the thingamajig"
         ...         pass
@@ -496,12 +515,16 @@ def _compile_uri_match_pattern(pattern):
 def get_file_type(fd):
     """
     Determine the file type of an open GenericFile instance.
+
     Parameters
     ----------
-    fd : GenericFile
+
+    fd : ``asdf.generic_io.GenericFile``
+
     Returns
     -------
-    FileType
+
+    `asdf.util.FileType`
     """
     if fd.peek(5) == constants.ASDF_MAGIC:
         return FileType.ASDF
@@ -514,7 +537,7 @@ def get_file_type(fd):
 
 class FileType(enum.Enum):
     """
-    Enum representing file types recognized by asdf.
+    Enum representing if a file is ASDF, FITS or UNKNOWN.
     """
 
     ASDF = 1
diff --git a/asdf/yamlutil.py b/asdf/yamlutil.py
index 67b681ef8..e4b1d5049 100644
--- a/asdf/yamlutil.py
+++ b/asdf/yamlutil.py
@@ -119,10 +119,10 @@ def represent_ordereddict(dumper, data):
 # Handle numpy scalars
 
 
-for scalar_type in util.iter_subclasses(np.floating):
+for scalar_type in util._iter_subclasses(np.floating):
     AsdfDumper.add_representer(scalar_type, lambda dumper, data: dumper.represent_float(float(data)))
 
-for scalar_type in util.iter_subclasses(np.integer):
+for scalar_type in util._iter_subclasses(np.integer):
     AsdfDumper.add_representer(scalar_type, lambda dumper, data: dumper.represent_int(int(data)))
 
 
diff --git a/docs/asdf/deprecations.rst b/docs/asdf/deprecations.rst
index 3b952870f..64f784cae 100644
--- a/docs/asdf/deprecations.rst
+++ b/docs/asdf/deprecations.rst
@@ -9,6 +9,16 @@ Deprecations
 Version 3.0
 ===========
 
+The following functions in ``asdf.util`` are deprecated:
+
+* ``human_list`` this is no longer part of the public API
+* ``resolve_name`` see ``astropy.utils.resolve_name``
+* ``minversion`` see ``astropy.utils.minversion``
+* ``iter_subclasses`` this is no longer part of the public API
+
+Version 3.0
+===========
+
 SerializationContext was previously importable from ``asdf.asdf.SerializationContext``.
 Although not part of the public API, this import path has been deprecated and users
 should instead import ``SerializationContext`` from `asdf.extension`.
diff --git a/pytest_asdf/plugin.py b/pytest_asdf/plugin.py
index 469cf7fe9..f556cd5bd 100644
--- a/pytest_asdf/plugin.py
+++ b/pytest_asdf/plugin.py
@@ -66,9 +66,7 @@ def from_parent(
         **kwargs,
     ):
         # Fix for depreciation of fspath in pytest 7+
-        from asdf.util import minversion
-
-        if minversion("pytest", "7.0.0"):
+        if pytest.__version__ >= "7.0.0":
             path = pathlib.Path(fspath)
             kwargs["path"] = path
         else: