diff --git a/misc/requirements/requirements-flake8.txt b/misc/requirements/requirements-flake8.txt
index 3128e63d8..7410107a1 100644
--- a/misc/requirements/requirements-flake8.txt
+++ b/misc/requirements/requirements-flake8.txt
@@ -2,7 +2,7 @@
 
 attrs==19.1.0
 entrypoints==0.3
-flake8==3.7.7
+flake8==3.7.8
 flake8-bugbear==19.3.0
 flake8-builtins==1.4.1
 flake8-comprehensions==2.1.0
@@ -19,7 +19,7 @@ flake8-tuple==0.4.0
 mccabe==0.6.1
 pep8-naming==0.8.2
 pycodestyle==2.5.0
-pydocstyle==3.0.0
+pydocstyle==3.0.0  # rq.filter: < 4
 pyflakes==2.1.1
 six==1.12.0
 snowballstemmer==1.9.0
diff --git a/misc/requirements/requirements-flake8.txt-raw b/misc/requirements/requirements-flake8.txt-raw
index 1bdca6974..1bc691a77 100644
--- a/misc/requirements/requirements-flake8.txt-raw
+++ b/misc/requirements/requirements-flake8.txt-raw
@@ -12,5 +12,8 @@ flake8-string-format
 flake8-tidy-imports
 flake8-tuple
 pep8-naming
-pydocstyle
+pydocstyle < 4
 pyflakes
+
+# WORKAROUND for https://gitlab.com/pycqa/flake8-docstrings/issues/36
+#@ filter: pydocstyle < 4
diff --git a/misc/requirements/requirements-mypy.txt b/misc/requirements/requirements-mypy.txt
index eac1123af..4d68606dc 100644
--- a/misc/requirements/requirements-mypy.txt
+++ b/misc/requirements/requirements-mypy.txt
@@ -1,8 +1,9 @@
 # This file is automatically generated by scripts/dev/recompile_requirements.py
 
-mypy==0.711
+mypy==0.720
 mypy-extensions==0.4.1
 # PyQt5==5.11.3
-# PyQt5-sip==4.19.17
+# PyQt5-sip==4.19.18
 -e git+https://github.com/qutebrowser/PyQt5-stubs.git@wip#egg=PyQt5_stubs
 typed-ast==1.4.0
+typing-extensions==3.7.4
diff --git a/misc/requirements/requirements-pip.txt b/misc/requirements/requirements-pip.txt
index e2336bba6..52eb8fad2 100644
--- a/misc/requirements/requirements-pip.txt
+++ b/misc/requirements/requirements-pip.txt
@@ -2,7 +2,7 @@
 
 appdirs==1.4.3
 packaging==19.0
-pyparsing==2.4.0
+pyparsing==2.4.2
 setuptools==41.0.1
 six==1.12.0
 wheel==0.33.4
diff --git a/misc/requirements/requirements-pyqt.txt b/misc/requirements/requirements-pyqt.txt
index be65f9815..0e8bcd476 100644
--- a/misc/requirements/requirements-pyqt.txt
+++ b/misc/requirements/requirements-pyqt.txt
@@ -2,4 +2,4 @@
 
 PyQt5==5.13.0
 PyQt5-sip==4.19.18
-PyQtWebEngine==5.12.1
+PyQtWebEngine==5.13.0
diff --git a/misc/requirements/requirements-pyroma.txt b/misc/requirements/requirements-pyroma.txt
index 608ff3944..a48aafaad 100644
--- a/misc/requirements/requirements-pyroma.txt
+++ b/misc/requirements/requirements-pyroma.txt
@@ -1,4 +1,4 @@
 # This file is automatically generated by scripts/dev/recompile_requirements.py
 
-docutils==0.14
+docutils==0.15
 pyroma==2.5
diff --git a/misc/requirements/requirements-sphinx.txt b/misc/requirements/requirements-sphinx.txt
index 97852e55e..e862537bf 100644
--- a/misc/requirements/requirements-sphinx.txt
+++ b/misc/requirements/requirements-sphinx.txt
@@ -4,14 +4,14 @@ alabaster==0.7.12
 Babel==2.7.0
 certifi==2019.6.16
 chardet==3.0.4
-docutils==0.14
+docutils==0.15
 idna==2.8
 imagesize==1.1.0
 Jinja2==2.10.1
 MarkupSafe==1.1.1
 packaging==19.0
 Pygments==2.4.2
-pyparsing==2.4.0
+pyparsing==2.4.2
 pytz==2019.1
 requests==2.22.0
 six==1.12.0
diff --git a/misc/requirements/requirements-tests.txt b/misc/requirements/requirements-tests.txt
index f63b687ea..3464be25a 100644
--- a/misc/requirements/requirements-tests.txt
+++ b/misc/requirements/requirements-tests.txt
@@ -3,32 +3,32 @@
 atomicwrites==1.3.0
 attrs==19.1.0
 backports.functools-lru-cache==1.5
-beautifulsoup4==4.7.1
+beautifulsoup4==4.8.0
 cheroot==6.5.5
 Click==7.0
 # colorama==0.4.1
 coverage==4.5.3
 EasyProcess==0.2.7
-Flask==1.0.3
+Flask==1.1.1
 glob2==0.7
 hunter==3.0.1
-hypothesis==4.24.6
+hypothesis==4.28.2
 importlib-metadata==0.18
 itsdangerous==1.1.0
 # Jinja2==2.10.1
-Mako==1.0.13
+Mako==1.0.14
 manhole==1.6.0
 # MarkupSafe==1.1.1
-more-itertools==7.1.0
+more-itertools==7.2.0
 packaging==19.0
 parse==1.12.0
-parse-type==0.4.2
+parse-type==0.5.2
 pluggy==0.12.0
 py==1.8.0
 py-cpuinfo==5.0.0
-pyparsing==2.4.0
-pytest==5.0.0
-pytest-bdd==3.1.0
+pyparsing==2.4.2
+pytest==5.0.1
+pytest-bdd==3.1.1
 pytest-benchmark==3.2.2
 pytest-cov==2.7.1
 pytest-instafail==0.4.1
@@ -43,5 +43,5 @@ six==1.12.0
 soupsieve==1.9.2
 vulture==1.0
 wcwidth==0.1.7
-Werkzeug==0.15.4
-zipp==0.5.1
+Werkzeug==0.15.5
+zipp==0.5.2
diff --git a/misc/requirements/requirements-tox.txt b/misc/requirements/requirements-tox.txt
index a4ab4892b..8ed7493dd 100644
--- a/misc/requirements/requirements-tox.txt
+++ b/misc/requirements/requirements-tox.txt
@@ -5,10 +5,10 @@ importlib-metadata==0.18
 packaging==19.0
 pluggy==0.12.0
 py==1.8.0
-pyparsing==2.4.0
+pyparsing==2.4.2
 six==1.12.0
 toml==0.10.0
 tox==3.13.2
 tox-venv==0.4.0
-virtualenv==16.6.1
+virtualenv==16.6.2
 zipp==0.5.2
diff --git a/mypy.ini b/mypy.ini
index 0607ddfdf..1880921b9 100644
--- a/mypy.ini
+++ b/mypy.ini
@@ -17,6 +17,7 @@ disallow_untyped_decorators = True
 # check_untyped_defs = True
 # no_implicit_optional = True
 # warn_return_any = True
+warn_unreachable = True
 
 # Other strictness flags
 strict_equality = True
diff --git a/qutebrowser/browser/browsertab.py b/qutebrowser/browser/browsertab.py
index 67fad967c..a5e1650e4 100644
--- a/qutebrowser/browser/browsertab.py
+++ b/qutebrowser/browser/browsertab.py
@@ -788,7 +788,9 @@ class AbstractTabPrivate:
         if cur_mode == usertypes.KeyMode.insert:
             return
 
-        def _auto_insert_mode_cb(elem: 'webelem.AbstractWebElement') -> None:
+        def _auto_insert_mode_cb(
+                elem: typing.Optional['webelem.AbstractWebElement']
+        ) -> None:
             """Called from JS after finding the focused element."""
             if elem is None:
                 log.webview.debug("No focused element!")
diff --git a/qutebrowser/browser/webengine/webenginesettings.py b/qutebrowser/browser/webengine/webenginesettings.py
index 84ad5d04b..7ccdc160d 100644
--- a/qutebrowser/browser/webengine/webenginesettings.py
+++ b/qutebrowser/browser/webengine/webenginesettings.py
@@ -26,6 +26,7 @@ Module attributes:
 
 import os
 import operator
+import typing  # pylint: disable=unused-import,useless-suppression
 
 from PyQt5.QtGui import QFont
 from PyQt5.QtWebEngineWidgets import (QWebEngineSettings, QWebEngineProfile,
@@ -37,9 +38,9 @@ from qutebrowser.config.websettings import AttributeInfo as Attr
 from qutebrowser.utils import utils, standarddir, qtutils, message, log
 
 # The default QWebEngineProfile
-default_profile = None
+default_profile = None  # type: typing.Optional[QWebEngineProfile]
 # The QWebEngineProfile used for private (off-the-record) windows
-private_profile = None
+private_profile = None  # type: typing.Optional[QWebEngineProfile]
 # The global WebEngineSettings object
 global_settings = None
 
diff --git a/qutebrowser/browser/webkit/webkitelem.py b/qutebrowser/browser/webkit/webkitelem.py
index 983904eeb..3b65fc7a6 100644
--- a/qutebrowser/browser/webkit/webkitelem.py
+++ b/qutebrowser/browser/webkit/webkitelem.py
@@ -172,7 +172,8 @@ class WebKitElement(webelem.AbstractWebElement):
     def _parent(self) -> typing.Optional['WebKitElement']:
         """Get the parent element of this element."""
         self._check_vanished()
-        elem = self._elem.parent()
+        elem = typing.cast(typing.Optional[QWebElement],
+                           self._elem.parent())
         if elem is None or elem.isNull():
             return None
         return WebKitElement(elem, tab=self._tab)
diff --git a/qutebrowser/commands/command.py b/qutebrowser/commands/command.py
index 044816fdb..02d546228 100644
--- a/qutebrowser/commands/command.py
+++ b/qutebrowser/commands/command.py
@@ -203,7 +203,7 @@ class Command:
         else:
             raise TypeError("{}: Invalid value={!r} for argument '{}'!"
                             .format(self.name, arg_info.value, param.name))
-        return False
+        raise utils.Unreachable
 
     def _inspect_func(self):
         """Inspect the function to get useful information from it.
diff --git a/qutebrowser/components/misccommands.py b/qutebrowser/components/misccommands.py
index fc5fce225..afc79e0a7 100644
--- a/qutebrowser/components/misccommands.py
+++ b/qutebrowser/components/misccommands.py
@@ -23,6 +23,7 @@ import os
 import signal
 import functools
 import logging
+import typing
 
 try:
     import hunter
@@ -37,7 +38,8 @@ from qutebrowser.api import cmdutils, apitypes, message, config
 
 @cmdutils.register(name='reload')
 @cmdutils.argument('tab', value=cmdutils.Value.count_tab)
-def reloadpage(tab: apitypes.Tab, force: bool = False) -> None:
+def reloadpage(tab: typing.Optional[apitypes.Tab],
+               force: bool = False) -> None:
     """Reload the current/[count]th tab.
 
     Args:
@@ -50,7 +52,7 @@ def reloadpage(tab: apitypes.Tab, force: bool = False) -> None:
 
 @cmdutils.register()
 @cmdutils.argument('tab', value=cmdutils.Value.count_tab)
-def stop(tab: apitypes.Tab) -> None:
+def stop(tab: typing.Optional[apitypes.Tab]) -> None:
     """Stop loading in the current/[count]th tab.
 
     Args:
@@ -90,7 +92,7 @@ def _print_pdf(tab: apitypes.Tab, filename: str) -> None:
 @cmdutils.register(name='print')
 @cmdutils.argument('tab', value=cmdutils.Value.count_tab)
 @cmdutils.argument('pdf', flag='f', metavar='file')
-def printpage(tab: apitypes.Tab,
+def printpage(tab: typing.Optional[apitypes.Tab],
               preview: bool = False, *,
               pdf: str = None) -> None:
     """Print the current/[count]th tab.
@@ -156,7 +158,7 @@ def insert_text(tab: apitypes.Tab, text: str) -> None:
     Args:
         text: The text to insert.
     """
-    def _insert_text_cb(elem: apitypes.WebElement) -> None:
+    def _insert_text_cb(elem: typing.Optional[apitypes.WebElement]) -> None:
         if elem is None:
             message.error("No element focused!")
             return
@@ -188,7 +190,7 @@ def click_element(tab: apitypes.Tab, filter_: str, value: str, *,
         target: How to open the clicked element (normal/tab/tab-bg/window).
         force_event: Force generating a fake click event.
     """
-    def single_cb(elem: apitypes.WebElement) -> None:
+    def single_cb(elem: typing.Optional[apitypes.WebElement]) -> None:
         """Click a single element."""
         if elem is None:
             message.error("No element found with id {}!".format(value))
@@ -229,7 +231,7 @@ def debug_webaction(tab: apitypes.Tab, action: str, count: int = 1) -> None:
 
 @cmdutils.register()
 @cmdutils.argument('tab', value=cmdutils.Value.count_tab)
-def tab_mute(tab: apitypes.Tab) -> None:
+def tab_mute(tab: typing.Optional[apitypes.Tab]) -> None:
     """Mute/Unmute the current/[count]th tab.
 
     Args:
diff --git a/qutebrowser/config/config.py b/qutebrowser/config/config.py
index 4eb6f2a1f..4159e1aec 100644
--- a/qutebrowser/config/config.py
+++ b/qutebrowser/config/config.py
@@ -187,7 +187,7 @@ class KeyConfig:
     def get_command(self,
                     key: keyutils.KeySequence,
                     mode: str,
-                    default: bool = False) -> str:
+                    default: bool = False) -> typing.Optional[str]:
         """Get the command for a given key (or None)."""
         self._validate(key, mode)
         if default:
@@ -202,7 +202,7 @@ class KeyConfig:
              mode: str,
              save_yaml: bool = False) -> None:
         """Add a new binding from key to command."""
-        if command is not None and not command.strip():
+        if not command.strip():
             raise configexc.KeybindingError(
                 "Can't add binding '{}' with empty command in {} "
                 'mode'.format(key, mode))
diff --git a/qutebrowser/config/configtypes.py b/qutebrowser/config/configtypes.py
index e43871ca6..de26d8321 100644
--- a/qutebrowser/config/configtypes.py
+++ b/qutebrowser/config/configtypes.py
@@ -740,7 +740,7 @@ class BoolAsk(Bool):
                  value: str) -> typing.Union[bool, str, None]:
         # basic validation unneeded if it's == 'ask' and done by Bool if we
         # call super().from_str
-        if isinstance(value, str) and value.lower() == 'ask':
+        if value.lower() == 'ask':
             return 'ask'
         return super().from_str(value)
 
@@ -1147,7 +1147,7 @@ class Font(BaseType):
     """
 
     # Gets set when the config is initialized.
-    monospace_fonts = None
+    monospace_fonts = None  # type: str
     font_regex = re.compile(r"""
         (
             (
@@ -1329,7 +1329,7 @@ class Regex(BaseType):
 
     def to_py(
             self,
-            value: typing.Union[str, typing.Pattern[str]]
+            value: typing.Union[str, typing.Pattern[str], configutils.Unset]
     ) -> typing.Union[configutils.Unset, None, typing.Pattern[str]]:
         """Get a compiled regex from either a string or a regex object."""
         self._basic_py_validation(value, (str, self._regex_type))
diff --git a/qutebrowser/mainwindow/tabwidget.py b/qutebrowser/mainwindow/tabwidget.py
index 7f6201f88..03fe6418c 100644
--- a/qutebrowser/mainwindow/tabwidget.py
+++ b/qutebrowser/mainwindow/tabwidget.py
@@ -19,6 +19,7 @@
 
 """The tab widget used for TabbedBrowser from browser.py."""
 
+import typing
 import functools
 import contextlib
 
@@ -347,7 +348,8 @@ class TabWidget(QTabWidget):
 
     def setTabIcon(self, idx: int, icon: QIcon):
         """Always show tab icons for pinned tabs in some circumstances."""
-        tab = self.widget(idx)
+        tab = typing.cast(typing.Optional[browsertab.AbstractTab],
+                          self.widget(idx))
         if (icon.isNull() and
                 config.cache['tabs.favicons.show'] != 'never' and
                 config.cache['tabs.pinned.shrink'] and
diff --git a/qutebrowser/misc/checkpyver.py b/qutebrowser/misc/checkpyver.py
index aab373648..597b2597c 100644
--- a/qutebrowser/misc/checkpyver.py
+++ b/qutebrowser/misc/checkpyver.py
@@ -49,7 +49,8 @@ def check_python_version():
         version_str = '.'.join(map(str, sys.version_info[:3]))
         text = ("At least Python 3.5 is required to run qutebrowser, but " +
                 "it's running with " + version_str + ".\n")
-        if Tk and '--no-err-windows' not in sys.argv:  # pragma: no cover
+        if (Tk and  # type: ignore
+                '--no-err-windows' not in sys.argv):  # pragma: no cover
             root = Tk()
             root.withdraw()
             messagebox.showerror("qutebrowser: Fatal error!", text)
diff --git a/qutebrowser/misc/crashsignal.py b/qutebrowser/misc/crashsignal.py
index 6bbd480f1..c645f19fd 100644
--- a/qutebrowser/misc/crashsignal.py
+++ b/qutebrowser/misc/crashsignal.py
@@ -172,7 +172,7 @@ class CrashHandler(QObject):
         if sys.__stderr__ is not None:
             faulthandler.enable(sys.__stderr__)
         else:
-            faulthandler.disable()
+            faulthandler.disable()  # type: ignore
         try:
             self._crash_log_file.close()
             os.remove(self._crash_log_file.name)
diff --git a/qutebrowser/utils/log.py b/qutebrowser/utils/log.py
index 004ce16c0..4d32d8222 100644
--- a/qutebrowser/utils/log.py
+++ b/qutebrowser/utils/log.py
@@ -259,7 +259,7 @@ def _init_handlers(level, color, force_color, json_logging, ram_capacity):
         level, color, force_color, json_logging)
 
     if sys.stderr is None:
-        console_handler = None
+        console_handler = None  # type: ignore
     else:
         strip = False if force_color else None
         if use_colorama:
@@ -313,7 +313,7 @@ def _init_formatters(level, color, force_color, json_logging):
     html_formatter = HTMLFormatter(EXTENDED_FMT_HTML, DATEFMT,
                                    log_colors=LOG_COLORS)
     if sys.stderr is None:
-        return None, ram_formatter, html_formatter, False
+        return None, ram_formatter, html_formatter, False  # type: ignore
 
     if json_logging:
         console_formatter = JSONFormatter()
diff --git a/qutebrowser/utils/version.py b/qutebrowser/utils/version.py
index 437ba49a3..615522c05 100644
--- a/qutebrowser/utils/version.py
+++ b/qutebrowser/utils/version.py
@@ -352,9 +352,9 @@ def _chromium_version():
     Also see https://www.chromium.org/developers/calendar
     and https://chromereleases.googleblog.com/
     """
-    if webenginesettings is None or QWebEngineProfile is None:
+    if webenginesettings is None or QWebEngineProfile is None:  # type: ignore
         # This should never happen
-        return 'unavailable'
+        return 'unavailable'  # type: ignore
     ua = webenginesettings.default_user_agent
     if ua is None:
         profile = QWebEngineProfile.defaultProfile()