diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
new file mode 100644
index 00000000..49b67a3c
--- /dev/null
+++ b/.github/workflows/test.yml
@@ -0,0 +1,22 @@
+name: Run tests
+
+on: [push, pull_request]
+
+jobs:
+  test-latest:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      matrix:
+        os: [macos-latest, ubuntu-latest, windows-latest]
+        python-version: [3.5, 3.6, 3.7, 3.8]
+
+    steps:
+    - uses: actions/checkout@v2
+    - name: Set up Python ${{ matrix.python-version }}
+      uses: actions/setup-python@v1
+      with:
+        python-version: ${{ matrix.python-version }}
+    - name: Install tox
+      run: python -m pip install --upgrade pip tox
+    - name: Run Tests
+      run: tox -e py,install,docs
diff --git a/docs/release_notes.rst b/docs/release_notes.rst
index 9e9c4f3f..b5f532a3 100644
--- a/docs/release_notes.rst
+++ b/docs/release_notes.rst
@@ -20,8 +20,10 @@ Bug Fixes
   The bug caused some argument names to go unreported in D417 (#448).
 * Fixed an issue where skipping errors on module level docstring via #noqa
   failed when there where more prior comments (#446).
+* Support backslash-continued descriptions in docstrings (#472).
 * Correctly detect publicity of modules inside directories (#470, #494).
 
+
 5.0.2 - January 8th, 2020
 ---------------------------
 
diff --git a/src/pydocstyle/checker.py b/src/pydocstyle/checker.py
index 8e3be2c4..cd2846e5 100644
--- a/src/pydocstyle/checker.py
+++ b/src/pydocstyle/checker.py
@@ -278,7 +278,9 @@ def check_indent(self, definition, docstring):
             indent = self._get_docstring_indent(definition, docstring)
             lines = docstring.split('\n')
             if len(lines) > 1:
-                lines = lines[1:]  # First line does not need indent.
+                # First line and line continuations need no indent.
+                lines = [line for i, line in enumerate(lines)
+                         if i and not lines[i-1].endswith('\\')]
                 indents = [leading_space(l) for l in lines if not is_blank(l)]
                 if set(' \t') == set(''.join(indents) + indent):
                     yield violations.D206()
@@ -703,7 +705,9 @@ def _check_parameters_section(docstring, definition, context):
         """
         docstring_args = set()
         section_level_indent = leading_space(context.line)
-        content = context.following_lines
+        # Join line continuations, then resplit by line.
+        content = (
+            '\n'.join(context.following_lines).replace('\\\n', '').split('\n'))
         for current_line, next_line in zip(content, content[1:]):
             # All parameter definitions in the Numpy parameters
             # section must be at the same indent level as the section
diff --git a/src/tests/test_cases/sections.py b/src/tests/test_cases/sections.py
index 2200ddfe..d671102b 100644
--- a/src/tests/test_cases/sections.py
+++ b/src/tests/test_cases/sections.py
@@ -389,7 +389,6 @@ def test_missing_docstring_another(skip, verbose):  # noqa: D213, D407
 @expect("D417: Missing argument descriptions in the docstring "
         "(argument(s) y are missing descriptions in "
         "'test_missing_numpy_args' docstring)")
-@expect("D207: Docstring is under-indented")
 def test_missing_numpy_args(_private_arg=0, x=1, y=2):  # noqa: D406, D407
     """Toggle the gizmo.
 
@@ -405,13 +404,19 @@ def test_missing_numpy_args(_private_arg=0, x=1, y=2):  # noqa: D406, D407
 class TestNumpy:  # noqa: D203
     """Test class."""
 
-    def test_method(self, test, another_test, _, x=1, y=2, _private_arg=1):  # noqa: D213, D407
+    def test_method(self, test, another_test, z, _, x=1, y=2, _private_arg=1):  # noqa: D213, D407
         """Test a valid args section.
 
+        Some long string with a \
+line continuation.
+
         Parameters
         ----------
         test, another_test
             Some parameters without type.
+        z : some parameter with a very long type description that requires a \
+line continuation.
+            But no further description.
         x, y : int
             Some integer parameters.
 
diff --git a/tox.ini b/tox.ini
index 3638f82c..91eacd46 100644
--- a/tox.ini
+++ b/tox.ini
@@ -4,7 +4,7 @@
 # install tox" and then run "tox" from this directory.
 
 [tox]
-envlist = {py35,py36,py37,py38}-{tests,install},py36-docs
+envlist = {py35,py36,py37,py38}-{tests,install},docs,install,py36-docs
 
 [testenv]
 download = true
@@ -20,34 +20,43 @@ deps =
     -rrequirements/runtime.txt
     -rrequirements/tests.txt
 
-[testenv:py37-install]
+[testenv:install]
 skip_install = True
 commands =
     python setup.py bdist_wheel
     pip install --no-index --find-links=dist pydocstyle
     pydocstyle --help
 
+[testenv:docs]
+changedir = docs
+deps =
+   -rrequirements/runtime.txt
+   -rrequirements/docs.txt
+commands = sphinx-build -b html . _build
+
+[testenv:py36-docs]
+changedir = {[testenv:docs]changedir}
+deps = {[testenv:docs]deps}
+commands = {[testenv:docs]commands}
+
 # There's no way to generate sub-sections in tox.
 # The following sections are all references to the `py37-install`.
 
 [testenv:py35-install]
-skip_install = {[testenv:py37-install]skip_install}
-commands = {[testenv:py37-install]commands}
+skip_install = {[testenv:install]skip_install}
+commands = {[testenv:install]commands}
 
 [testenv:py36-install]
-skip_install = {[testenv:py37-install]skip_install}
-commands = {[testenv:py37-install]commands}
+skip_install = {[testenv:install]skip_install}
+commands = {[testenv:install]commands}
 
-[testenv:py38-install]
-skip_install = {[testenv:py37-install]skip_install}
-commands = {[testenv:py37-install]commands}
+[testenv:py37-install]
+skip_install = {[testenv:install]skip_install}
+commands = {[testenv:install]commands}
 
-[testenv:py36-docs]
-changedir=docs
-deps =
-   -rrequirements/runtime.txt
-   -rrequirements/docs.txt
-commands=sphinx-build -b html . _build
+[testenv:py38-install]
+skip_install = {[testenv:install]skip_install}
+commands = {[testenv:install]commands}
 
 [pytest]
 pep8ignore =