diff --git a/src/sphinx_autodoc_typehints/__init__.py b/src/sphinx_autodoc_typehints/__init__.py
index 2311133d..997c93e1 100644
--- a/src/sphinx_autodoc_typehints/__init__.py
+++ b/src/sphinx_autodoc_typehints/__init__.py
@@ -4,6 +4,7 @@
 import re
 import sys
 import textwrap
+import types
 from ast import FunctionDef, Module, stmt
 from typing import Any, AnyStr, Callable, ForwardRef, NewType, TypeVar, get_type_hints
 
@@ -21,8 +22,16 @@
 _LOGGER = logging.getLogger(__name__)
 _PYDATA_ANNOTATIONS = {"Any", "AnyStr", "Callable", "ClassVar", "Literal", "NoReturn", "Optional", "Tuple", "Union"}
 
+# types has a bunch of things like ModuleType where ModuleType.__module__ is
+# "builtins" and ModuleType.__name__ is "module", so we have to check for this.
+_TYPES_DICT = {getattr(types, name): name for name in types.__all__}
+# Prefer FunctionType to LambdaType (they are synonymous)
+_TYPES_DICT[types.FunctionType] = "FunctionType"
+
 
 def get_annotation_module(annotation: Any) -> str:
+    if annotation in _TYPES_DICT:
+        return "types"
     if annotation is None:
         return "builtins"
     is_new_type = sys.version_info >= (3, 10) and isinstance(annotation, NewType)
@@ -35,17 +44,22 @@ def get_annotation_module(annotation: Any) -> str:
     raise ValueError(f"Cannot determine the module of {annotation}")
 
 
+def _is_newtype(annotation: Any) -> bool:
+    if sys.version_info < (3, 10):
+        return inspect.isfunction(annotation) and hasattr(annotation, "__supertype__")
+    else:
+        return isinstance(annotation, NewType)
+
+
 def get_annotation_class_name(annotation: Any, module: str) -> str:
     # Special cases
     if annotation is None:
         return "None"
-    elif annotation is Any:
-        return "Any"
-    elif annotation is AnyStr:
+    if annotation is AnyStr:
         return "AnyStr"
-    elif (sys.version_info < (3, 10) and inspect.isfunction(annotation) and hasattr(annotation, "__supertype__")) or (
-        sys.version_info >= (3, 10) and isinstance(annotation, NewType)
-    ):
+    if annotation in _TYPES_DICT:
+        return _TYPES_DICT[annotation]
+    if _is_newtype(annotation):
         return "NewType"
 
     if getattr(annotation, "__qualname__", None):
diff --git a/tests/test_sphinx_autodoc_typehints.py b/tests/test_sphinx_autodoc_typehints.py
index 2e213dd1..6d2728b1 100644
--- a/tests/test_sphinx_autodoc_typehints.py
+++ b/tests/test_sphinx_autodoc_typehints.py
@@ -4,6 +4,7 @@
 import pathlib
 import re
 import sys
+import types
 import typing
 from functools import cmp_to_key
 from io import StringIO
@@ -134,6 +135,10 @@ def __getitem__(self, params):
     [
         pytest.param(str, "builtins", "str", (), id="str"),
         pytest.param(None, "builtins", "None", (), id="None"),
+        pytest.param(ModuleType, "types", "ModuleType", (), id="ModuleType"),
+        pytest.param(FunctionType, "types", "FunctionType", (), id="FunctionType"),
+        pytest.param(types.CodeType, "types", "CodeType", (), id="CodeType"),
+        pytest.param(types.CoroutineType, "types", "CoroutineType", (), id="CoroutineType"),
         pytest.param(Any, "typing", "Any", (), id="Any"),
         pytest.param(AnyStr, "typing", "AnyStr", (), id="AnyStr"),
         pytest.param(Dict, "typing", "Dict", (), id="Dict"),
@@ -170,9 +175,10 @@ def __getitem__(self, params):
     ],
 )
 def test_parse_annotation(annotation: Any, module: str, class_name: str, args: tuple[Any, ...]) -> None:
-    assert get_annotation_module(annotation) == module
-    assert get_annotation_class_name(annotation, module) == class_name
-    assert get_annotation_args(annotation, module, class_name) == args
+    got_mod = get_annotation_module(annotation)
+    got_cls = get_annotation_class_name(annotation, module)
+    got_args = get_annotation_args(annotation, module, class_name)
+    assert (got_mod, got_cls, got_args) == (module, class_name, args)
 
 
 @pytest.mark.parametrize(
@@ -181,6 +187,8 @@ def test_parse_annotation(annotation: Any, module: str, class_name: str, args: t
         (str, ":py:class:`str`"),
         (int, ":py:class:`int`"),
         (StringIO, ":py:class:`~io.StringIO`"),
+        (FunctionType, ":py:class:`~types.FunctionType`"),
+        (ModuleType, ":py:class:`~types.ModuleType`"),
         (type(None), ":py:obj:`None`"),
         (type, ":py:class:`type`"),
         (collections.abc.Callable, ":py:class:`~collections.abc.Callable`"),
diff --git a/whitelist.txt b/whitelist.txt
index be15dbcd..d32e390f 100644
--- a/whitelist.txt
+++ b/whitelist.txt
@@ -4,6 +4,7 @@ autouse
 backfill
 conf
 contravariant
+Coroutine
 cpython
 csv
 dedent
@@ -31,7 +32,9 @@ iterdir
 kwonlyargs
 libs
 metaclass
+ModuleType
 multiline
+newtype
 nptyping
 param
 parametrized