diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 898dfe5..5cb06d9 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -33,6 +33,16 @@ jobs:
           - os: ubuntu-latest
             python-version: "3.11-dev"
             deps: test
+          # Installing optional dependencies stuff takes ages on PyPy
+          - os: ubuntu-latest
+            python-version: "pypy-3.8"
+            deps: test
+          - os: windows-latest
+            python-version: "pypy-3.8"
+            deps: test
+          - os: macos-latest
+            python-version: "pypy-3.8"
+            deps: test
 
     steps:
     - uses: actions/checkout@v2
diff --git a/IPython/core/tests/test_async_helpers.py b/IPython/core/tests/test_async_helpers.py
index 9ca67f4..40a840c 100644
--- a/IPython/core/tests/test_async_helpers.py
+++ b/IPython/core/tests/test_async_helpers.py
@@ -3,6 +3,7 @@ Test for async helpers.
 
 Should only trigger on python 3.5+ or will have syntax errors.
 """
+import platform
 from itertools import chain, repeat
 from textwrap import dedent, indent
 from unittest import TestCase
@@ -275,7 +276,7 @@ class AsyncTest(TestCase):
         """
         )
 
-    if sys.version_info < (3,9):
+    if sys.version_info < (3, 9) and platform.python_implementation() != "PyPy":
         # new pgen parser in 3.9 does not raise MemoryError on too many nested
         # parens anymore
         def test_memory_error(self):
diff --git a/IPython/core/tests/test_debugger.py b/IPython/core/tests/test_debugger.py
index 65bcb5e..75ce9fd 100644
--- a/IPython/core/tests/test_debugger.py
+++ b/IPython/core/tests/test_debugger.py
@@ -371,11 +371,13 @@ def _decorator_skip_setup():
     child = pexpect.spawn(
         sys.executable, ["-m", "IPython", "--colors=nocolor"], env=env
     )
-    child.timeout = 5 * IPYTHON_TESTING_TIMEOUT_SCALE
+    child.timeout = 15 * IPYTHON_TESTING_TIMEOUT_SCALE
 
     child.expect("IPython")
     child.expect("\n")
 
+    child.timeout = 5 * IPYTHON_TESTING_TIMEOUT_SCALE
+
     dedented_blocks = [dedent(b).strip() for b in skip_decorators_blocks]
     in_prompt_number = 1
     for cblock in dedented_blocks:
@@ -448,11 +450,13 @@ def test_decorator_skip_with_breakpoint():
     child = pexpect.spawn(
         sys.executable, ["-m", "IPython", "--colors=nocolor"], env=env
     )
-    child.timeout = 5 * IPYTHON_TESTING_TIMEOUT_SCALE
+    child.timeout = 15 * IPYTHON_TESTING_TIMEOUT_SCALE
 
     child.expect("IPython")
     child.expect("\n")
 
+    child.timeout = 5 * IPYTHON_TESTING_TIMEOUT_SCALE
+
     ### we need a filename, so we need to exec the full block with a filename
     with NamedTemporaryFile(suffix=".py", dir=".", delete=True) as tf:
 
diff --git a/IPython/core/tests/test_magic.py b/IPython/core/tests/test_magic.py
index 428d711..aa006f6 100644
--- a/IPython/core/tests/test_magic.py
+++ b/IPython/core/tests/test_magic.py
@@ -2,6 +2,7 @@
 """Tests for various magic functions."""
 
 import asyncio
+import gc
 import io
 import os
 import re
@@ -576,6 +577,7 @@ class TestXdel(tt.TempFileMixin):
         _ip.magic("xdel a")
 
         # Check that a's __del__ method has been called.
+        gc.collect(0)
         assert monitor == [1]
 
 def doctest_who():
diff --git a/IPython/core/tests/test_run.py b/IPython/core/tests/test_run.py
index a872f5a..0f73a78 100644
--- a/IPython/core/tests/test_run.py
+++ b/IPython/core/tests/test_run.py
@@ -18,6 +18,7 @@ as otherwise it may influence later tests.
 
 import functools
 import os
+import platform
 from os.path import join as pjoin
 import random
 import string
@@ -158,7 +159,7 @@ def doctest_reset_del():
 
     In [3]: a = A()
 
-    In [4]: get_ipython().reset()
+    In [4]: get_ipython().reset(); import gc; x = gc.collect(0)
     Hi
 
     In [5]: 1+1
@@ -241,6 +242,10 @@ class TestMagicRunSimple(tt.TempFileMixin):
         _ip.run_cell("t = isinstance(f(), foo)")
         assert _ip.user_ns["t"] is True
 
+    @pytest.mark.xfail(
+        platform.python_implementation() == "PyPy",
+        reason="expecting __del__ call on exit is unreliable and doesn't happen on PyPy",
+    )
     def test_obj_del(self):
         """Test that object's __del__ methods are called on exit."""
         src = ("class A(object):\n"
@@ -286,14 +291,20 @@ class TestMagicRunSimple(tt.TempFileMixin):
             _ip.magic("run %s" % empty.fname)
             assert _ip.user_ns["afunc"]() == 1
 
-    @dec.skip_win32
     def test_tclass(self):
         mydir = os.path.dirname(__file__)
-        tc = os.path.join(mydir, 'tclass')
-        src = ("%%run '%s' C-first\n"
-               "%%run '%s' C-second\n"
-               "%%run '%s' C-third\n") % (tc, tc, tc)
-        self.mktmp(src, '.ipy')
+        tc = os.path.join(mydir, "tclass")
+        src = f"""\
+import gc
+%run "{tc}" C-first
+gc.collect(0)
+%run "{tc}" C-second
+gc.collect(0)
+%run "{tc}" C-third
+gc.collect(0)
+%reset -f
+"""
+        self.mktmp(src, ".ipy")
         out = """\
 ARGV 1-: ['C-first']
 ARGV 1-: ['C-second']
diff --git a/IPython/core/tests/test_ultratb.py b/IPython/core/tests/test_ultratb.py
index d0f13df..66a7a95 100644
--- a/IPython/core/tests/test_ultratb.py
+++ b/IPython/core/tests/test_ultratb.py
@@ -3,6 +3,7 @@
 """
 import io
 import logging
+import platform
 import re
 import sys
 import os.path
@@ -248,7 +249,8 @@ bar()
                 ip.showsyntaxerror()
 
 import sys
-if sys.version_info < (3,9):
+
+if sys.version_info < (3, 9) and platform.python_implementation() != "PyPy":
     """
     New 3.9 Pgen Parser does not raise Memory error, except on failed malloc.
     """
@@ -359,7 +361,7 @@ def r3o2():
         ):
             ip.run_cell("r1()")
 
-    @recursionlimit(200)
+    @recursionlimit(160)
     def test_recursion_three_frames(self):
         with tt.AssertPrints("[... skipping similar frames: "), \
                 tt.AssertPrints(re.compile(r"r3a at line 8 \(\d{2} times\)"), suppress=False), \
diff --git a/IPython/extensions/tests/test_autoreload.py b/IPython/extensions/tests/test_autoreload.py
index e03a08e..8cc55e7 100644
--- a/IPython/extensions/tests/test_autoreload.py
+++ b/IPython/extensions/tests/test_autoreload.py
@@ -13,6 +13,8 @@
 # -----------------------------------------------------------------------------
 
 import os
+import platform
+import pytest
 import sys
 import tempfile
 import textwrap
@@ -28,6 +30,12 @@ from unittest import TestCase
 from IPython.extensions.autoreload import AutoreloadMagics
 from IPython.core.events import EventManager, pre_run_cell
 
+if platform.python_implementation() == "PyPy":
+    pytest.skip(
+        "Current autoreload implementation is extremly slow on PyPy",
+        allow_module_level=True,
+    )
+
 # -----------------------------------------------------------------------------
 # Test fixture
 # -----------------------------------------------------------------------------
diff --git a/IPython/terminal/tests/test_debug_magic.py b/IPython/terminal/tests/test_debug_magic.py
index d19f827..faa3b7c 100644
--- a/IPython/terminal/tests/test_debug_magic.py
+++ b/IPython/terminal/tests/test_debug_magic.py
@@ -51,6 +51,8 @@ def test_debug_magic_passes_through_generators():
     child.sendline("    pass")
     child.sendline("")
 
+    child.timeout = 10 * IPYTHON_TESTING_TIMEOUT_SCALE
+
     child.expect('Exception:')
 
     child.expect(in_prompt)
diff --git a/IPython/terminal/tests/test_embed.py b/IPython/terminal/tests/test_embed.py
index ac4c942..3f0885e 100644
--- a/IPython/terminal/tests/test_embed.py
+++ b/IPython/terminal/tests/test_embed.py
@@ -74,8 +74,9 @@ def test_nest_embed():
 
     child = pexpect.spawn(sys.executable, ['-m', 'IPython', '--colors=nocolor'],
                           env=env)
-    child.timeout = 5 * IPYTHON_TESTING_TIMEOUT_SCALE
+    child.timeout = 15 * IPYTHON_TESTING_TIMEOUT_SCALE
     child.expect(ipy_prompt)
+    child.timeout = 5 * IPYTHON_TESTING_TIMEOUT_SCALE
     child.sendline("import IPython")
     child.expect(ipy_prompt)
     child.sendline("ip0 = get_ipython()")
diff --git a/IPython/testing/plugin/show_refs.py b/IPython/testing/plugin/show_refs.py
deleted file mode 100644
index b2c70ad..0000000
--- a/IPython/testing/plugin/show_refs.py
+++ /dev/null
@@ -1,19 +0,0 @@
-"""Simple script to show reference holding behavior.
-
-This is used by a companion test case.
-"""
-
-import gc
-
-class C(object):
-   def __del__(self):
-      pass
-      #print 'deleting object...'  # dbg
-
-if __name__ == '__main__':
-   c = C()
-
-   c_refs = gc.get_referrers(c)
-   ref_ids = list(map(id,c_refs))
-
-   print('c referrers:',list(map(type,c_refs)))
diff --git a/IPython/testing/plugin/test_refs.py b/IPython/testing/plugin/test_refs.py
index bd7ad8f..b92448b 100644
--- a/IPython/testing/plugin/test_refs.py
+++ b/IPython/testing/plugin/test_refs.py
@@ -37,10 +37,3 @@ def doctest_ivars():
     In [6]: zz
     Out[6]: 1
     """
-
-def doctest_refs():
-    """DocTest reference holding issues when running scripts.
-
-    In [32]: run show_refs.py
-    c referrers: [<... 'dict'>]
-    """
diff --git a/IPython/utils/ipstruct.py b/IPython/utils/ipstruct.py
index d71a75e..ed11210 100644
--- a/IPython/utils/ipstruct.py
+++ b/IPython/utils/ipstruct.py
@@ -131,7 +131,7 @@ class Struct(dict):
         >>> s.a
         10
         >>> type(s.get)
-        <... 'builtin_function_or_method'>
+        <...method'>
         >>> try:
         ...     s.b
         ... except AttributeError: