diff --git a/docs/conda.yml b/docs/conda.yml
new file mode 100644
index 0000000000..e33288db2a
--- /dev/null
+++ b/docs/conda.yml
@@ -0,0 +1,8 @@
+# TODO: remove when RTD supports python 3.7 without conda
+name: tornado-docs
+dependencies:
+  - python=3.7
+  - pip:
+    - sphinx
+    - sphinx-rtd-theme
+    - Twisted
diff --git a/docs/conf.py b/docs/conf.py
index de2f60cfa5..d6e37faf4f 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -1,14 +1,14 @@
 # Ensure we get the local copy of tornado instead of what's on the standard path
 import os
 import sys
-import time
+
 sys.path.insert(0, os.path.abspath(".."))
 import tornado
 
 master_doc = "index"
 
 project = "Tornado"
-copyright = "2009-%s, The Tornado Authors" % time.strftime("%Y")
+copyright = "The Tornado Authors"
 
 version = release = tornado.version
 
@@ -20,8 +20,8 @@
     "sphinx.ext.viewcode",
 ]
 
-primary_domain = 'py'
-default_role = 'py:obj'
+primary_domain = "py"
+default_role = "py:obj"
 
 autodoc_member_order = "bysource"
 autoclass_content = "both"
@@ -42,14 +42,12 @@
 coverage_ignore_classes = [
     # tornado.gen
     "Runner",
-
     # tornado.web
     "ChunkedTransferEncoding",
     "GZipContentEncoding",
     "OutputTransform",
     "TemplateModule",
     "url",
-
     # tornado.websocket
     "WebSocketProtocol",
     "WebSocketProtocol13",
@@ -60,32 +58,36 @@
     # various modules
     "doctests",
     "main",
-
     # tornado.escape
     # parse_qs_bytes should probably be documented but it's complicated by
     # having different implementations between py2 and py3.
     "parse_qs_bytes",
-
     # tornado.gen
     "Multi",
 ]
 
-html_favicon = 'favicon.ico'
+html_favicon = "favicon.ico"
 
 latex_documents = [
-    ('index', 'tornado.tex', 'Tornado Documentation', 'The Tornado Authors', 'manual', False),
+    (
+        "index",
+        "tornado.tex",
+        "Tornado Documentation",
+        "The Tornado Authors",
+        "manual",
+        False,
+    )
 ]
 
-intersphinx_mapping = {
-    'python': ('https://docs.python.org/3.6/', None),
-}
+intersphinx_mapping = {"python": ("https://docs.python.org/3.6/", None)}
 
-on_rtd = os.environ.get('READTHEDOCS', None) == 'True'
+on_rtd = os.environ.get("READTHEDOCS", None) == "True"
 
 # On RTD we can't import sphinx_rtd_theme, but it will be applied by
 # default anyway.  This block will use the same theme when building locally
 # as on RTD.
 if not on_rtd:
     import sphinx_rtd_theme
-    html_theme = 'sphinx_rtd_theme'
+
+    html_theme = "sphinx_rtd_theme"
     html_theme_path = [sphinx_rtd_theme.get_html_theme_path()]
diff --git a/docs/requirements.txt b/docs/requirements.txt
index d5626da3cf..69c93b12cc 100644
--- a/docs/requirements.txt
+++ b/docs/requirements.txt
@@ -1,4 +1,3 @@
-# https://bugs.python.org/issue34700
-sphinx<1.8.0
+sphinx>1.8.2
 sphinx_rtd_theme
 Twisted
diff --git a/maint/requirements.in b/maint/requirements.in
index 094f7ca50c..87caccd2a0 100644
--- a/maint/requirements.in
+++ b/maint/requirements.in
@@ -11,7 +11,7 @@ pycares
 pycurl
 
 # Other useful tools
-Sphinx<1.8.0
+Sphinx>1.8.2
 autopep8
 black
 coverage
diff --git a/maint/requirements.txt b/maint/requirements.txt
index 17b8f37867..f8d3399399 100644
--- a/maint/requirements.txt
+++ b/maint/requirements.txt
@@ -41,7 +41,7 @@ requests==2.20.0
 requests-toolbelt==0.8.0
 six==1.11.0
 snowballstemmer==1.2.1
-Sphinx==1.7.9
+Sphinx==1.8.3
 sphinx-rtd-theme==0.4.2
 sphinxcontrib-websupport==1.1.0
 toml==0.10.0
diff --git a/readthedocs.yml b/readthedocs.yml
new file mode 100644
index 0000000000..e40382080b
--- /dev/null
+++ b/readthedocs.yml
@@ -0,0 +1,4 @@
+# TODO: remove when RTD supports Python 3.7 without conda.
+# https://github.com/rtfd/readthedocs-docker-images/pull/73
+conda:
+  file: docs/conda.yml