python
@@ -127,6 +127,14 @@ def test_any_works_with_alias(self):
 class BottomTypeTestsMixin:
     bottom_type: ClassVar[Any]
 
+    def test_equality(self):
+        self.assertEqual(self.bottom_type, self.bottom_type)
+        self.assertIs(self.bottom_type, self.bottom_type)
+        self.assertNotEqual(self.bottom_type, None)
+
+    def test_get_origin(self):
+        self.assertIs(get_origin(self.bottom_type), None)
+
     def test_instance_type_error(self):
         with self.assertRaises(TypeError):
             isinstance(42, self.bottom_type)
@@ -162,13 +170,35 @@ class NoReturnTests(BottomTypeTestsMixin, BaseTestCase):
     def test_repr(self):
         self.assertEqual(repr(NoReturn), 'typing.NoReturn')
 
+    def test_get_type_hints(self):
+        def some(arg: NoReturn) -> NoReturn: ...
+        def some_str(arg: 'NoReturn') -> 'typing.NoReturn': ...
+
+        expected = {'arg': NoReturn, 'return': NoReturn}
+        for target in [some, some_str]:
+            with self.subTest(target=target):
+                self.assertEqual(gth(target), expected)
+
+    def test_not_equality(self):
+        self.assertNotEqual(NoReturn, Never)
+        self.assertNotEqual(Never, NoReturn)
+
 
 class NeverTests(BottomTypeTestsMixin, BaseTestCase):
     bottom_type = Never
 
     def test_repr(self):
         self.assertEqual(repr(Never), 'typing.Never')
 
+    def test_get_type_hints(self):
+        def some(arg: Never) -> Never: ...
+        def some_str(arg: 'Never') -> 'typing.Never': ...
+
+        expected = {'arg': Never, 'return': Never}
+        for target in [some, some_str]:
+            with self.subTest(target=target):
+                self.assertEqual(gth(target), expected)
+
 
 class AssertNeverTests(BaseTestCase):
     def test_exception(self):
@@ -177,11 +207,23 @@ def test_exception(self):
 
 
 class SelfTests(BaseTestCase):
+    def test_equality(self):
+        self.assertEqual(Self, Self)
+        self.assertIs(Self, Self)
+        self.assertNotEqual(Self, None)
+
     def test_basics(self):
         class Foo:
             def bar(self) -> Self: ...
+        class FooStr:
+            def bar(self) -> 'Self': ...
+        class FooStrTyping:
+            def bar(self) -> 'typing.Self': ...
 
-        self.assertEqual(gth(Foo.bar), {'return': Self})
+        for target in [Foo, FooStr, FooStrTyping]:
+            with self.subTest(target=target):
+                self.assertEqual(gth(target.bar), {'return': Self})
+        self.assertIs(get_origin(Self), None)
 
     def test_repr(self):
         self.assertEqual(repr(Self), 'typing.Self')
@@ -194,6 +236,9 @@ def test_cannot_subclass(self):
         with self.assertRaises(TypeError):
             class C(type(Self)):
                 pass
+        with self.assertRaises(TypeError):
+            class C(Self):
+                pass
 
     def test_cannot_init(self):
         with self.assertRaises(TypeError):
@@ -5295,11 +5340,13 @@ def test_special_attrs(self):
             typing.Literal: 'Literal',
             typing.NewType: 'NewType',
             typing.NoReturn: 'NoReturn',
+            typing.Never: 'Never',
             typing.Optional: 'Optional',
             typing.TypeAlias: 'TypeAlias',
             typing.TypeGuard: 'TypeGuard',
             typing.TypeVar: 'TypeVar',
             typing.Union: 'Union',
+            typing.Self: 'Self',
             # Subscribed special forms
             typing.Annotated[Any, "Annotation"]: 'Annotated',
             typing.ClassVar[Any]: 'ClassVar',