diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 4a97af8..9a0201f 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -11,12 +11,12 @@ on:
 
 jobs:
   test:
-    name: test py${{ matrix.python-version }} on ${{ matrix.os }}
+    name: test py-${{ matrix.python-version }} on ${{ matrix.os }}
     strategy:
       fail-fast: false
       matrix:
         os: [ubuntu, macos]
-        python-version: ['3.7', '3.8', '3.9', '3.10']
+        python-version: ['3.7', '3.8', '3.9', '3.10', 'pypy-3.7', 'pypy-3.8', 'pypy-3.9']
 
     runs-on: ${{ matrix.os }}-latest
 
@@ -39,10 +39,10 @@ jobs:
         key: ${{ runner.os }}-${{ env.pythonLocation }}-${{ hashFiles('pyproject.toml') }}-${{ hashFiles('tests/requirements.txt') }}
 
     - run: pip install -r tests/requirements.txt
-      if: steps.cache.outputs.cache-hit != 'true'
+#      if: steps.cache.outputs.cache-hit != 'true'  # breaks pypy tests
 
     - run: poetry install
-      if: steps.cache.outputs.cache-hit != 'true'
+#      if: steps.cache.outputs.cache-hit != 'true'  # breaks pypy tests
 
     - run: make test
 
diff --git a/dirty_equals/_dict.py b/dirty_equals/_dict.py
index 0731279..965d7eb 100644
--- a/dirty_equals/_dict.py
+++ b/dirty_equals/_dict.py
@@ -121,7 +121,8 @@ def _filter_dict(self, d: Dict[Any, Any]) -> Dict[Any, Any]:
         return {k: v for k, v in d.items() if not self._ignore_value(v)}
 
     def _ignore_value(self, v: Any) -> bool:
-        if isinstance(v, (DirtyEquals, DirtyEqualsMeta)):
+        # `isinstance(v, (DirtyEquals, DirtyEqualsMeta))` seems to always return `True` on pypy, no idea why
+        if type(v) in (DirtyEquals, DirtyEqualsMeta):
             return False
         elif callable(self.ignore):
             return self.ignore(v)
diff --git a/docs/usage.md b/docs/usage.md
index 4506d63..260ab49 100644
--- a/docs/usage.md
+++ b/docs/usage.md
@@ -23,6 +23,10 @@ assert ['a', 'b', 'c'] == ~Contains('z')
 
 ## Initialised vs. Class comparison
 
+!!! warning
+
+    This does not work with PyPy.
+
 *dirty-equals* allows comparison with types regardless of whether they've been initialised.
 
 This saves users adding `()` in lots of places.
diff --git a/tests/test_base.py b/tests/test_base.py
index c0163b6..f411bed 100644
--- a/tests/test_base.py
+++ b/tests/test_base.py
@@ -1,3 +1,5 @@
+import platform
+
 import pytest
 
 from dirty_equals import Contains, IsApprox, IsInt, IsNegative, IsOneOf, IsPositive, IsStr
@@ -58,6 +60,7 @@ def test_dict_compare():
     assert v == {'foo': IsInt() & IsApprox(1), 'bar': IsPositive() | IsNegative(), 'spam': ~IsStr()}
 
 
+@pytest.mark.skipif(platform.python_implementation() == 'PyPy', reason='PyPy does not metaclass dunder methods')
 def test_not_repr():
     v = ~IsInt
     assert str(v) == '~IsInt'
@@ -68,6 +71,16 @@ def test_not_repr():
     assert str(v) == '~IsInt'
 
 
+def test_not_repr_instance():
+    v = ~IsInt()
+    assert str(v) == '~IsInt()'
+
+    with pytest.raises(AssertionError):
+        assert 1 == v
+
+    assert str(v) == '~IsInt()'
+
+
 def test_repr():
     v = ~IsInt
     assert str(v) == '~IsInt'
diff --git a/tests/test_boolean.py b/tests/test_boolean.py
index a8946b5..d89b601 100644
--- a/tests/test_boolean.py
+++ b/tests/test_boolean.py
@@ -1,3 +1,5 @@
+import platform
+
 import pytest
 
 from dirty_equals import IsFalseLike, IsTrueLike
@@ -43,11 +45,17 @@ def test_is_false_like_repr():
     assert repr(IsFalseLike(allow_strings=True)) == 'IsFalseLike(allow_strings=True)'
 
 
+@pytest.mark.skipif(platform.python_implementation() == 'PyPy', reason='PyPy does not metaclass dunder methods')
 def test_dirty_not_equals():
     with pytest.raises(AssertionError):
         assert 0 != IsFalseLike
 
 
+def test_dirty_not_equals_instance():
+    with pytest.raises(AssertionError):
+        assert 0 != IsFalseLike()
+
+
 def test_invalid_initialization():
     with pytest.raises(TypeError, match='takes 1 positional argument but 2 were given'):
         IsFalseLike(True)
diff --git a/tests/test_docs.py b/tests/test_docs.py
index cb325b4..3114b40 100644
--- a/tests/test_docs.py
+++ b/tests/test_docs.py
@@ -1,4 +1,5 @@
 import importlib.util
+import platform
 import re
 from pathlib import Path
 from textwrap import dedent
@@ -65,5 +66,6 @@ def pytest_generate_tests(metafunc):
     metafunc.parametrize('module_name,source_code', generate_code_chunks('dirty_equals', 'docs'))
 
 
+@pytest.mark.skipif(platform.python_implementation() == 'PyPy', reason='PyPy does not metaclass dunder methods')
 def test_docs_examples(module_name, source_code, import_execute):
     import_execute(module_name, source_code, True)
diff --git a/tests/test_inspection.py b/tests/test_inspection.py
index eb791f4..2698cb0 100644
--- a/tests/test_inspection.py
+++ b/tests/test_inspection.py
@@ -74,8 +74,8 @@ def test_has_name(value, dirty):
     'value,dirty',
     [
         (Foo(1, 2), HasAttributes(a=1, b=2)),
-        (Foo(1, 's'), HasAttributes(a=IsInt, b=IsStr)),
-        (Foo(1, 2), ~HasAttributes(a=IsInt, b=IsStr)),
+        (Foo(1, 's'), HasAttributes(a=IsInt(), b=IsStr())),
+        (Foo(1, 2), ~HasAttributes(a=IsInt(), b=IsStr())),
         (Foo(1, 2), ~HasAttributes(a=1, b=2, c=3)),
         (Foo(1, 2), HasAttributes(a=1, b=2, spam=AnyThing)),
         (Foo(1, 2), ~HasAttributes(a=1, b=2, missing=AnyThing)),