diff --git a/CHANGES.rst b/CHANGES.rst
index cbe5a09b0..26cb1b935 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -17,6 +17,9 @@
 - Add support for ASDF Standard 1.5.0, which includes several new
   transform schemas. [#776]
 
+- Enable validation and serialization of previously unhandled numpy
+  scalar types. [#778]
+
 2.5.2 (2020-02-28)
 ------------------
 
diff --git a/asdf/compat/numpycompat.py b/asdf/compat/numpycompat.py
index 79e38320d..45e679777 100644
--- a/asdf/compat/numpycompat.py
+++ b/asdf/compat/numpycompat.py
@@ -1,7 +1,8 @@
 from ..util import minversion
 
 
-__all__ = ['NUMPY_LT_1_7']
+__all__ = ['NUMPY_LT_1_7', 'NUMPY_LT_1_14']
 
 
 NUMPY_LT_1_7 = not minversion('numpy', '1.7.0')
+NUMPY_LT_1_14 = not minversion('numpy', '1.14.0')
diff --git a/asdf/schema.py b/asdf/schema.py
index 6665620c7..baa350b7a 100644
--- a/asdf/schema.py
+++ b/asdf/schema.py
@@ -16,6 +16,7 @@
 from jsonschema.exceptions import ValidationError
 
 import yaml
+import numpy as np
 
 from . import constants
 from . import generic_io
@@ -213,10 +214,11 @@ def _create_validator(validators=YAML_VALIDATORS):
     if JSONSCHEMA_LT_3:
         base_cls = mvalidators.create(meta_schema=meta_schema, validators=validators)
     else:
-        type_checker = mvalidators.Draft4Validator.TYPE_CHECKER.redefine(
-            'array',
-            lambda checker, instance: isinstance(instance, list) or isinstance(instance, tuple)
-        )
+        type_checker = mvalidators.Draft4Validator.TYPE_CHECKER.redefine_many({
+            'array': lambda checker, instance: isinstance(instance, list) or isinstance(instance, tuple),
+            'integer': lambda checker, instance: not isinstance(instance, bool) and isinstance(instance, Integral),
+            'string': lambda checker, instance: isinstance(instance, (str, np.str_)),
+        })
         id_of = mvalidators.Draft4Validator.ID_OF
         base_cls = mvalidators.create(
             meta_schema=meta_schema,
@@ -229,6 +231,8 @@ class ASDFValidator(base_cls):
         if JSONSCHEMA_LT_3:
             DEFAULT_TYPES = base_cls.DEFAULT_TYPES.copy()
             DEFAULT_TYPES['array'] = (list, tuple)
+            DEFAULT_TYPES['integer'] = (Integral)
+            DEFAULT_TYPES['string'] = (str, np.str_)
 
         def iter_errors(self, instance, _schema=None, _seen=set()):
             # We can't validate anything that looks like an external reference,
diff --git a/asdf/tests/test_schema.py b/asdf/tests/test_schema.py
index 1a265efe1..98a2f9b26 100644
--- a/asdf/tests/test_schema.py
+++ b/asdf/tests/test_schema.py
@@ -878,3 +878,48 @@ def test_nonexistent_tag(tmpdir):
             assert str(w[0].message).startswith("Unable to locate schema file")
             assert str(w[1].message).startswith("Unable to locate schema file")
             assert str(w[2].message).startswith(af['a']._tag)
+
+
+@pytest.mark.parametrize("numpy_value,valid_types", [
+    (np.str_("foo"), {"string"}),
+    (np.bytes_("foo"), set()),
+    (np.float16(3.14), {"number"}),
+    (np.float32(3.14159), {"number"}),
+    (np.float64(3.14159), {"number"}),
+    # Evidently float128 is not available on Windows:
+    (getattr(np, "float128", np.float64)(3.14159), {"number"}),
+    (np.int8(42), {"number", "integer"}),
+    (np.int16(42), {"number", "integer"}),
+    (np.int32(42), {"number", "integer"}),
+    (np.longlong(42), {"number", "integer"}),
+    (np.uint8(42), {"number", "integer"}),
+    (np.uint16(42), {"number", "integer"}),
+    (np.uint32(42), {"number", "integer"}),
+    (np.uint64(42), {"number", "integer"}),
+    (np.ulonglong(42), {"number", "integer"}),
+])
+def test_numpy_scalar_type_validation(numpy_value, valid_types):
+    def _assert_validation(jsonschema_type, expected_valid):
+        validator = schema.get_validator()
+        try:
+            validator.validate(numpy_value, _schema={"type": jsonschema_type})
+        except ValidationError:
+            valid = False
+        else:
+            valid = True
+
+        if valid is not expected_valid:
+            if expected_valid:
+                description = "valid"
+            else:
+                description = "invalid"
+            assert False, "Expected numpy.{} to be {} against jsonschema type '{}'".format(
+                type(numpy_value).__name__, description, jsonschema_type
+            )
+
+    for jsonschema_type in valid_types:
+        _assert_validation(jsonschema_type, True)
+
+    invalid_types = {"string", "number", "integer", "boolean", "null", "object"} - valid_types
+    for jsonschema_type in invalid_types:
+        _assert_validation(jsonschema_type, False)
diff --git a/asdf/tests/test_yaml.py b/asdf/tests/test_yaml.py
index 05e728da9..cc7d4a0c9 100644
--- a/asdf/tests/test_yaml.py
+++ b/asdf/tests/test_yaml.py
@@ -14,6 +14,8 @@
 import asdf
 from asdf import tagged
 from asdf import treeutil
+from asdf import yamlutil
+from asdf.compat.numpycompat import NUMPY_LT_1_14
 
 from . import helpers
 
@@ -275,3 +277,36 @@ class SomeObject:
     tag = 'tag:nowhere.org:none/some/thing'
     instance = tagged.tag_object(tag, SomeObject())
     assert instance._tag == tag
+
+
+@pytest.mark.parametrize("numpy_value,expected_value", [
+    (np.str_("foo"), "foo"),
+    (np.bytes_("foo"), b"foo"),
+    (np.float16(3.14), 3.14),
+    (np.float32(3.14159), 3.14159),
+    (np.float64(3.14159), 3.14159),
+    # Evidently float128 is not available on Windows:
+    (getattr(np, "float128", np.float64)(3.14159), 3.14159),
+    (np.int8(42), 42),
+    (np.int16(42), 42),
+    (np.int32(42), 42),
+    (np.int64(42), 42),
+    (np.longlong(42), 42),
+    (np.uint8(42), 42),
+    (np.uint16(42), 42),
+    (np.uint32(42), 42),
+    (np.uint64(42), 42),
+    (np.ulonglong(42), 42),
+])
+def test_numpy_scalar(numpy_value, expected_value):
+    ctx = asdf.AsdfFile()
+    tree = {"value": numpy_value}
+    buffer = io.BytesIO()
+
+    yamlutil.dump_tree(tree, buffer, ctx)
+    buffer.seek(0)
+
+    if isinstance(expected_value, float) and NUMPY_LT_1_14:
+        assert yamlutil.load_tree(buffer, ctx)["value"] == pytest.approx(expected_value, rel=0.001)
+    else:
+        assert yamlutil.load_tree(buffer, ctx)["value"] == expected_value
diff --git a/asdf/yamlutil.py b/asdf/yamlutil.py
index 552b7852a..7248a06ea 100644
--- a/asdf/yamlutil.py
+++ b/asdf/yamlutil.py
@@ -218,6 +218,15 @@ def represent_ordereddict(dumper, data):
 for scalar_type in util.iter_subclasses(np.integer):
     AsdfDumper.add_representer(scalar_type, AsdfDumper.represent_int)
 
+def represent_numpy_str(dumper, data):
+    # The CSafeDumper implementation will raise an error if it
+    # doesn't recognize data as a string.  The Python SafeDumper
+    # has no problem with np.str_.
+    return dumper.represent_str(str(data))
+
+AsdfDumper.add_representer(np.str_, represent_numpy_str)
+AsdfDumper.add_representer(np.bytes_, AsdfDumper.represent_binary)
+
 
 def custom_tree_to_tagged_tree(tree, ctx):
     """