diff --git a/.github/workflows/testing.yml b/.github/workflows/testing.yml
index 6a56b47e..1abca4ea 100644
--- a/.github/workflows/testing.yml
+++ b/.github/workflows/testing.yml
@@ -12,7 +12,7 @@ jobs:
     steps:
     - uses: actions/checkout@v4
     - name: Set up Python 3.11
-      uses: actions/setup-python@v4
+      uses: actions/setup-python@v5
       with:
         python-version: 3.11
     - name: Install pre-commit
@@ -29,7 +29,7 @@ jobs:
     strategy:
       matrix:
         os: [ubuntu-latest, windows-latest, macos-latest]
-        python_version: ["3.8", "3.9", "3.10", "3.11", "3.12", "pypy-3.9"]
+        python_version: ["3.8", "3.9", "3.10", "3.11", "3.12", "3.13", "pypy-3.9"]
         exclude:
           # Do not test all minor versions on all platforms, especially if they
           # are not the oldest/newest supported versions
@@ -50,7 +50,7 @@ jobs:
     steps:
     - uses: actions/checkout@v4
     - name: Set up Python ${{ matrix.python_version }}
-      uses: actions/setup-python@v4
+      uses: actions/setup-python@v5
       with:
         python-version: ${{ matrix.python_version }}
         allow-prereleases: true
@@ -91,7 +91,7 @@ jobs:
     steps:
     - uses: actions/checkout@v4
     - name: Set up Python
-      uses: actions/setup-python@v4
+      uses: actions/setup-python@v5
       with:
         python-version: ${{ matrix.python_version }}
     - name: Install project and dependencies
@@ -127,7 +127,7 @@ jobs:
     steps:
     - uses: actions/checkout@v4
     - name: Set up Python
-      uses: actions/setup-python@v4
+      uses: actions/setup-python@v5
       with:
         python-version: ${{ matrix.python_version }}
     - name: Install project and dependencies
@@ -155,7 +155,7 @@ jobs:
     steps:
     - uses: actions/checkout@v4
     - name: Set up Python
-      uses: actions/setup-python@v4
+      uses: actions/setup-python@v5
       with:
         python-version: ${{ matrix.python_version }}
     - name: Install downstream project and dependencies
@@ -180,7 +180,7 @@ jobs:
     steps:
     - uses: actions/checkout@v4
     - name: Set up Python
-      uses: actions/setup-python@v4
+      uses: actions/setup-python@v5
       with:
         python-version: ${{ matrix.python_version }}
     - name: Install project and tests dependencies
diff --git a/dev-requirements.txt b/dev-requirements.txt
index 933e6909..35c529fe 100644
--- a/dev-requirements.txt
+++ b/dev-requirements.txt
@@ -9,7 +9,7 @@ psutil
 tornado
 # To be able to test numpy specific things
 # but do not build numpy from source on Python nightly
-numpy >=1.18.5; python_version <= '3.8'
+numpy >=1.18.5; python_version <= '3.12'
 # Code coverage uploader for Travis:
 codecov
 coverage
diff --git a/tests/cloudpickle_test.py b/tests/cloudpickle_test.py
index af5ef3e3..c7daaef2 100644
--- a/tests/cloudpickle_test.py
+++ b/tests/cloudpickle_test.py
@@ -1506,7 +1506,10 @@ def test_importing_multiprocessing_does_not_impact_whichmodule(self):
         )
         out, _ = proc.communicate()
         self.assertEqual(proc.wait(), 0)
-        self.assertEqual(out, b"numpy.core._multiarray_umath\n")
+        assert out.strip() in (
+            b"numpy.core._multiarray_umath",  # numpy 1
+            b"numpy._core._multiarray_umath",  # numpy 2
+        )
 
     def test_unrelated_faulty_module(self):
         # Check that pickling a dynamically defined function or class does not
@@ -2484,6 +2487,12 @@ def inner_function():
         inner_func = depickled_factory()
         assert inner_func() == _TEST_GLOBAL_VARIABLE
 
+    @pytest.mark.skipif(
+        sys.version_info < (3, 9),
+        reason="Can cause CPython 3.8 to segfault",
+    )
+    # TODO: remove this xfail when we drop support for Python 3.8. We don't
+    # plan to fix it because Python 3.8 is EOL.
     def test_recursion_during_pickling(self):
         class A:
             def __getattribute__(self, name):
diff --git a/tox.ini b/tox.ini
index 5985d534..a9d3eded 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py{38, 39, 310, 311, 312, py3}
+envlist = py{38, 39, 310, 311, 312, 313, py3}
 
 [testenv]
 deps = -rdev-requirements.txt