diff --git a/.github/workflows/ci_crontests.yml b/.github/workflows/ci_crontests.yml
index 4e24c8adb8..641050c1b2 100644
--- a/.github/workflows/ci_crontests.yml
+++ b/.github/workflows/ci_crontests.yml
@@ -43,6 +43,11 @@ jobs:
             toxargs: -v
             toxposargs: -v
 
+          - name: Documentation build with linkcheck
+            os: ubuntu-latest
+            python: '3.10'
+            toxenv: linkcheck
+
     steps:
     - name: Checkout code
       uses: actions/checkout@v3
diff --git a/README.rst b/README.rst
index e92ce67303..eab5562b4a 100644
--- a/README.rst
+++ b/README.rst
@@ -45,7 +45,7 @@ Installation and Requirements
 Astroquery works with Python 3.7 or later.
 As an `astropy`_ affiliate, astroquery requires `astropy`_ version 4.0 or later.
 
-astroquery uses the `requests <http://docs.python-requests.org/en/latest/>`_
+astroquery uses the `requests <https://requests.readthedocs.io/en/latest/>`_
 module to communicate with the internet.  `BeautifulSoup
 <http://www.crummy.com/software/BeautifulSoup/>`_ and `html5lib'
 <https://html5lib.readthedocs.io/en/latest/>`_ are needed for HTML parsing for
diff --git a/astroquery/alfalfa/__init__.py b/astroquery/alfalfa/__init__.py
index 29f8372419..36c3feb7d6 100644
--- a/astroquery/alfalfa/__init__.py
+++ b/astroquery/alfalfa/__init__.py
@@ -5,8 +5,6 @@
 
 :Author: Jordan Mirocha (mirochaj@gmail.com)
 
-This package is for querying the ALFALFA data repository hosted at
-http://arecibo.tc.cornell.edu/hiarchive/alfalfa/
 """
 import warnings
 
diff --git a/astroquery/hips2fits/core.py b/astroquery/hips2fits/core.py
index 56e5a8df0c..f034c625b1 100644
--- a/astroquery/hips2fits/core.py
+++ b/astroquery/hips2fits/core.py
@@ -167,7 +167,7 @@ def query(self, hips, width, height, projection, ra, dec, fov, coordsys="icrs",
         * The center of projection in world coordinates (ra, dec)
         * The fov angle in world coordinates
         * The rotation angle of the projection
-        * The name of the projection. All `astropy projections <https://docs.astropy.org/en/stable/wcs/#supported-projections>`_ are supported:
+        * The name of the projection. All `astropy projections <https://docs.astropy.org/en/stable/wcs/supported_projections.html>`_ are supported:
 
         Parameters
         ----------
@@ -181,7 +181,7 @@ def query(self, hips, width, height, projection, ra, dec, fov, coordsys="icrs",
             Height in pixels of the output image.
         projection : str
             Name of the requested projection, eg: SIN, TAN, MOL, AIT, CAR, CEA, STG	Compulsory if wcs is not provided.
-            See `this page <https://docs.astropy.org/en/stable/wcs/#supported-projections>`_ for an exhaustive list.
+            See `this page <https://docs.astropy.org/en/stable/wcs/supported_projections.html>`_ for an exhaustive list.
         fov : `~astropy.coordinates.Angle`
             Size (FoV) of the cutout on the sky.
             This is the size of the largest dimension of the image.
diff --git a/docs/index.rst b/docs/index.rst
index d6f81acb8f..7e0432bee1 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -87,7 +87,7 @@ The following packages are required for astroquery installation & use:
 * `numpy <http://www.numpy.org>`_ >= 1.16
 * `astropy <http://www.astropy.org>`__ (>=4)
 * `pyVO`_ (>=1.1)
-* `requests <http://docs.python-requests.org/en/latest/>`_
+* `requests <https://requests.readthedocs.io/en/latest/>`_
 * `keyring <https://pypi.python.org/pypi/keyring>`_
 * `Beautiful Soup <https://www.crummy.com/software/BeautifulSoup/>`_
 * `html5lib <https://pypi.python.org/pypi/html5lib>`_
diff --git a/tox.ini b/tox.ini
index c7a3467b65..b0c0c82a19 100644
--- a/tox.ini
+++ b/tox.ini
@@ -2,6 +2,7 @@
 envlist =
     py{37,38,39,310}-test{,-alldeps,-oldestdeps,-devdeps,-predeps}{,-online}{,-cov}
     codestyle
+    linkcheck
     build_docs
 requires =
     setuptools >= 30.3.0
@@ -71,3 +72,12 @@ requires =
 commands =
     pip freeze
     python setup.py build_sphinx -W
+
+
+[testenv:linkcheck]
+changedir = {toxinidir}
+description = check the links in the HTML docs
+extras = docs
+commands =
+    pip freeze
+    python setup.py build_sphinx -W -b linkcheck