diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 3eb1ce80..b34018a1 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -27,14 +27,14 @@ jobs:
       matrix:
         os: [ubuntu-latest]
         python-version: [3.6, 3.7, 3.8, 3.9]
-        sphinx: [">=3,<4"]
+        sphinx: [">=3,<4", ">=4,<5"]
         include:
-          - os: ubuntu-latest
-            python-version: 3.8
-            sphinx: ">=2,<3"
           - os: windows-latest
             python-version: 3.7
             sphinx: ">=3,<4"
+          - os: macos-latest
+            python-version: 3.9
+            sphinx: ">=4,<5"
 
     runs-on: ${{ matrix.os }}
 
diff --git a/setup.cfg b/setup.cfg
index 02997266..dfaeb482 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -38,7 +38,7 @@ project_urls =
 [options]
 packages = find:
 install_requires =
-    docutils>=0.15
+    docutils>=0.15,<0.18
     importlib_metadata
     ipython
     ipywidgets>=7.0.0,<8
@@ -48,7 +48,7 @@ install_requires =
     nbconvert>=5.6,<7
     nbformat~=5.0
     pyyaml
-    sphinx>=2,<4
+    sphinx>=3.1,<5
     sphinx-togglebutton~=0.2.2
 python_requires = >=3.6
 include_package_data = True
diff --git a/tests/conftest.py b/tests/conftest.py
index 9147190f..12e8353b 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -5,6 +5,7 @@
 
 import nbformat as nbf
 import pytest
+import sphinx
 from docutils.nodes import image as image_node
 from nbconvert.filters import strip_ansi
 from nbdime.diffing.notebooks import (
@@ -60,6 +61,9 @@ def __init__(self, app, filenames):
         self.app = app
         self.env = app.env
         self.files = [os.path.splitext(ff) for ff in filenames]
+        self.software_versions = (
+            f".sphinx{sphinx.version_info[0]}"  # software version tracking for fixtures
+        )
 
         # self.nb_file = nb_file
         # self.nb_name = os.path.splitext(nb_file)[0]
diff --git a/tests/test_glue.py b/tests/test_glue.py
index 96935e3a..ffd7fbf5 100644
--- a/tests/test_glue.py
+++ b/tests/test_glue.py
@@ -110,7 +110,11 @@ def test_parser(sphinx_run, clean_doctree, file_regression):
     # print(sphinx_run.status())
     assert sphinx_run.warnings() == ""
     doctree = clean_doctree(sphinx_run.get_resolved_doctree("with_glue"))
-    file_regression.check(doctree.pformat(), extension=".xml", encoding="utf8")
+    file_regression.check(
+        doctree.pformat(),
+        extension=f"{sphinx_run.software_versions}.xml",
+        encoding="utf8",
+    )
     glue_domain = NbGlueDomain.from_env(sphinx_run.app.env)
     assert set(glue_domain.cache) == {
         "key_text1",
diff --git a/tests/test_glue/test_parser.xml b/tests/test_glue/test_parser.sphinx3.xml
similarity index 100%
rename from tests/test_glue/test_parser.xml
rename to tests/test_glue/test_parser.sphinx3.xml
diff --git a/tests/test_glue/test_parser.sphinx4.xml b/tests/test_glue/test_parser.sphinx4.xml
new file mode 100644
index 00000000..eff7afc6
--- /dev/null
+++ b/tests/test_glue/test_parser.sphinx4.xml
@@ -0,0 +1,169 @@
+<document source="with_glue">
+    <section classes="tex2jax_ignore mathjax_ignore" ids="glue-tests" names="glue\ tests">
+        <title>
+            Glue Tests
+        <CellNode cell_type="code" classes="cell">
+            <CellInputNode classes="cell_input">
+                <literal_block language="ipython3" linenos="False" xml:space="preserve">
+                    from myst_nb import glue
+        <CellNode cell_type="code" classes="cell">
+            <CellInputNode classes="cell_input">
+                <literal_block language="ipython3" linenos="False" xml:space="preserve">
+                    glue("key_text1", "text1")
+                    glue("key_float", 3.14159)
+            <CellOutputNode classes="cell_output">
+                <literal_block classes="output text_plain" language="myst-ansi" linenos="False" xml:space="preserve">
+                    'text1'
+                <literal_block classes="output text_plain" language="myst-ansi" linenos="False" xml:space="preserve">
+                    3.14159
+        <CellNode cell_type="code" classes="cell">
+            <CellInputNode classes="cell_input">
+                <literal_block language="ipython3" linenos="False" xml:space="preserve">
+                    glue("key_undisplayed", "undisplayed", display=False)
+            <CellOutputNode classes="cell_output">
+        <CellNode cell_type="code" classes="cell">
+            <CellInputNode classes="cell_input">
+                <literal_block language="ipython3" linenos="False" xml:space="preserve">
+                    import pandas as pd
+                    df = pd.DataFrame({"header": [1, 2, 3]})
+                    glue("key_df", df)
+            <CellOutputNode classes="cell_output">
+                <raw classes="output text_html" format="html" xml:space="preserve">
+                    <div>
+                    <style scoped>
+                        .dataframe tbody tr th:only-of-type {
+                            vertical-align: middle;
+                        }
+                    
+                        .dataframe tbody tr th {
+                            vertical-align: top;
+                        }
+                    
+                        .dataframe thead th {
+                            text-align: right;
+                        }
+                    </style>
+                    <table border="1" class="dataframe">
+                      <thead>
+                        <tr style="text-align: right;">
+                          <th></th>
+                          <th>header</th>
+                        </tr>
+                      </thead>
+                      <tbody>
+                        <tr>
+                          <th>0</th>
+                          <td>1</td>
+                        </tr>
+                        <tr>
+                          <th>1</th>
+                          <td>2</td>
+                        </tr>
+                        <tr>
+                          <th>2</th>
+                          <td>3</td>
+                        </tr>
+                      </tbody>
+                    </table>
+                    </div>
+        <CellNode cell_type="code" classes="cell">
+            <CellInputNode classes="cell_input">
+                <literal_block language="ipython3" linenos="False" xml:space="preserve">
+                    import matplotlib.pyplot as plt
+                    plt.plot([1, 2, 3])
+                    glue("key_plt", plt.gcf(), display=False)
+            <CellOutputNode classes="cell_output">
+                <image candidates="{'*': '_build/jupyter_execute/with_glue_5_1.png'}" uri="_build/jupyter_execute/with_glue_5_1.png">
+        <section ids="referencing-the-figs" names="referencing\ the\ figs">
+            <title>
+                Referencing the figs
+            <paragraph>
+                <inline classes="pasted-inline">
+                    <literal classes="output text_plain" language="none">
+                        'text1'
+                , 
+                <inline classes="pasted-inline">
+                    <image candidates="{'*': '_build/jupyter_execute/with_glue_5_0.png'}" uri="_build/jupyter_execute/with_glue_5_0.png">
+            <CellOutputNode classes="cell_output">
+                <raw classes="output text_html" format="html" xml:space="preserve">
+                    <div>
+                    <style scoped>
+                        .dataframe tbody tr th:only-of-type {
+                            vertical-align: middle;
+                        }
+                    
+                        .dataframe tbody tr th {
+                            vertical-align: top;
+                        }
+                    
+                        .dataframe thead th {
+                            text-align: right;
+                        }
+                    </style>
+                    <table border="1" class="dataframe">
+                      <thead>
+                        <tr style="text-align: right;">
+                          <th></th>
+                          <th>header</th>
+                        </tr>
+                      </thead>
+                      <tbody>
+                        <tr>
+                          <th>0</th>
+                          <td>1</td>
+                        </tr>
+                        <tr>
+                          <th>1</th>
+                          <td>2</td>
+                        </tr>
+                        <tr>
+                          <th>2</th>
+                          <td>3</td>
+                        </tr>
+                      </tbody>
+                    </table>
+                    </div>
+            <paragraph>
+                and 
+                <inline classes="pasted-text">
+                    text1
+                 inline…
+            <paragraph>
+                and formatted 
+                <inline classes="pasted-text">
+                    3.14
+            <CellOutputNode classes="cell_output">
+                <image candidates="{'*': '_build/jupyter_execute/with_glue_5_0.png'}" uri="_build/jupyter_execute/with_glue_5_0.png">
+            <paragraph>
+                and 
+                <inline classes="pasted-text">
+                    undisplayed
+                 inline…
+            <figure ids="abc" names="abc">
+                <CellOutputNode classes="cell_output">
+                    <image candidates="{'*': '_build/jupyter_execute/with_glue_5_0.png'}" uri="_build/jupyter_execute/with_glue_5_0.png">
+                <caption>
+                    A caption….
+                    
+                    ```## A test title 
+                    <inline classes="pasted-inline">
+                        <literal classes="output text_plain" language="none">
+                            'text1'
+        <section ids="math" names="math">
+            <title>
+                Math
+            <CellNode cell_type="code" classes="cell">
+                <CellInputNode classes="cell_input">
+                    <literal_block language="ipython3" linenos="False" xml:space="preserve">
+                        import sympy as sym
+                        f = sym.Function('f')
+                        y = sym.Function('y')
+                        n = sym.symbols(r'\alpha')
+                        f = y(n)-2*y(n-1/sym.pi)-5*y(n-2)
+                        glue("sym_eq", sym.rsolve(f,y(n),[1,4]))
+                <CellOutputNode classes="cell_output">
+                    <math_block classes="output text_latex" nowrap="False" number="True" xml:space="preserve">
+                        \displaystyle \left(\sqrt{5} i\right)^{\alpha} \left(\frac{1}{2} - \frac{2 \sqrt{5} i}{5}\right) + \left(- \sqrt{5} i\right)^{\alpha} \left(\frac{1}{2} + \frac{2 \sqrt{5} i}{5}\right)
+            <target refid="equation-eq-sym">
+            <math_block classes="pasted-math" docname="with_glue" ids="equation-eq-sym" label="eq-sym" nowrap="False" number="1" xml:space="preserve">
+                \displaystyle \left(\sqrt{5} i\right)^{\alpha} \left(\frac{1}{2} - \frac{2 \sqrt{5} i}{5}\right) + \left(- \sqrt{5} i\right)^{\alpha} \left(\frac{1}{2} + \frac{2 \sqrt{5} i}{5}\right)
diff --git a/tox.ini b/tox.ini
index 152376ae..fa70650b 100644
--- a/tox.ini
+++ b/tox.ini
@@ -13,11 +13,11 @@
 [tox]
 envlist = py37-sphinx3
 
-[testenv:py{36,37,38,39}-sphinx{2,3}]
+[testenv:py{36,37,38,39}-sphinx{3,4}]
 extras = testing
 deps =
-    sphinx2: sphinx>=2,<3
     sphinx3: sphinx>=3,<4
+    sphinx4: sphinx>=4,<5
 commands = pytest {posargs}
 
 [testenv:docs-{update,clean}]