diff --git a/homeassistant/core.py b/homeassistant/core.py
index 2553dbea74e..c8c5fc4d499 100644
--- a/homeassistant/core.py
+++ b/homeassistant/core.py
@@ -486,7 +486,7 @@ class Event:
     def __init__(
         self,
         event_type: str,
-        data: Optional[Dict] = None,
+        data: Optional[Dict[str, Any]] = None,
         origin: EventOrigin = EventOrigin.local,
         time_fired: Optional[int] = None,
         context: Optional[Context] = None,
@@ -550,9 +550,7 @@ class EventBus:
     @property
     def listeners(self) -> Dict[str, int]:
         """Return dictionary with events and the number of listeners."""
-        return run_callback_threadsafe(  # type: ignore
-            self._hass.loop, self.async_listeners
-        ).result()
+        return run_callback_threadsafe(self._hass.loop, self.async_listeners).result()
 
     def fire(
         self,
@@ -852,7 +850,7 @@ class StateMachine:
         future = run_callback_threadsafe(
             self._loop, self.async_entity_ids, domain_filter
         )
-        return future.result()  # type: ignore
+        return future.result()
 
     @callback
     def async_entity_ids(self, domain_filter: Optional[str] = None) -> List[str]:
@@ -873,9 +871,7 @@ class StateMachine:
 
     def all(self) -> List[State]:
         """Create a list of all states."""
-        return run_callback_threadsafe(  # type: ignore
-            self._loop, self.async_all
-        ).result()
+        return run_callback_threadsafe(self._loop, self.async_all).result()
 
     @callback
     def async_all(self) -> List[State]:
@@ -905,7 +901,7 @@ class StateMachine:
 
         Returns boolean to indicate if an entity was removed.
         """
-        return run_callback_threadsafe(  # type: ignore
+        return run_callback_threadsafe(
             self._loop, self.async_remove, entity_id
         ).result()
 
@@ -1064,9 +1060,7 @@ class ServiceRegistry:
     @property
     def services(self) -> Dict[str, Dict[str, Service]]:
         """Return dictionary with per domain a list of available services."""
-        return run_callback_threadsafe(  # type: ignore
-            self._hass.loop, self.async_services
-        ).result()
+        return run_callback_threadsafe(self._hass.loop, self.async_services).result()
 
     @callback
     def async_services(self) -> Dict[str, Dict[str, Service]]:
diff --git a/homeassistant/helpers/condition.py b/homeassistant/helpers/condition.py
index 3500a3a4e3d..363d33b14ea 100644
--- a/homeassistant/helpers/condition.py
+++ b/homeassistant/helpers/condition.py
@@ -146,19 +146,16 @@ def numeric_state(
     variables: TemplateVarsType = None,
 ) -> bool:
     """Test a numeric state condition."""
-    return cast(
-        bool,
-        run_callback_threadsafe(
-            hass.loop,
-            async_numeric_state,
-            hass,
-            entity,
-            below,
-            above,
-            value_template,
-            variables,
-        ).result(),
-    )
+    return run_callback_threadsafe(
+        hass.loop,
+        async_numeric_state,
+        hass,
+        entity,
+        below,
+        above,
+        value_template,
+        variables,
+    ).result()
 
 
 def async_numeric_state(
@@ -353,12 +350,9 @@ def template(
     hass: HomeAssistant, value_template: Template, variables: TemplateVarsType = None
 ) -> bool:
     """Test if template condition matches."""
-    return cast(
-        bool,
-        run_callback_threadsafe(
-            hass.loop, async_template, hass, value_template, variables
-        ).result(),
-    )
+    return run_callback_threadsafe(
+        hass.loop, async_template, hass, value_template, variables
+    ).result()
 
 
 def async_template(
diff --git a/homeassistant/helpers/discovery.py b/homeassistant/helpers/discovery.py
index ea20d8c9216..11663672bb2 100644
--- a/homeassistant/helpers/discovery.py
+++ b/homeassistant/helpers/discovery.py
@@ -10,11 +10,10 @@ from typing import Any, Callable, Collection, Dict, Optional, Union
 from homeassistant import core, setup
 from homeassistant.const import ATTR_DISCOVERED, ATTR_SERVICE, EVENT_PLATFORM_DISCOVERED
 from homeassistant.exceptions import HomeAssistantError
+from homeassistant.helpers.typing import ConfigType, DiscoveryInfoType
 from homeassistant.loader import DEPENDENCY_BLACKLIST, bind_hass
 from homeassistant.util.async_ import run_callback_threadsafe
 
-# mypy: allow-untyped-defs, no-check-untyped-defs
-
 EVENT_LOAD_PLATFORM = "load_platform.{}"
 ATTR_PLATFORM = "platform"
 
@@ -56,13 +55,29 @@ def async_listen(
 
 
 @bind_hass
-def discover(hass, service, discovered, component, hass_config):
+def discover(
+    hass: core.HomeAssistant,
+    service: str,
+    discovered: DiscoveryInfoType,
+    component: str,
+    hass_config: ConfigType,
+) -> None:
     """Fire discovery event. Can ensure a component is loaded."""
-    hass.add_job(async_discover(hass, service, discovered, component, hass_config))
+    hass.add_job(
+        async_discover(  # type: ignore
+            hass, service, discovered, component, hass_config
+        )
+    )
 
 
 @bind_hass
-async def async_discover(hass, service, discovered, component, hass_config):
+async def async_discover(
+    hass: core.HomeAssistant,
+    service: str,
+    discovered: Optional[DiscoveryInfoType],
+    component: Optional[str],
+    hass_config: ConfigType,
+) -> None:
     """Fire discovery event. Can ensure a component is loaded."""
     if component in DEPENDENCY_BLACKLIST:
         raise HomeAssistantError(f"Cannot discover the {component} component.")
@@ -70,7 +85,7 @@ async def async_discover(hass, service, discovered, component, hass_config):
     if component is not None and component not in hass.config.components:
         await setup.async_setup_component(hass, component, hass_config)
 
-    data = {ATTR_SERVICE: service}
+    data: Dict[str, Any] = {ATTR_SERVICE: service}
 
     if discovered is not None:
         data[ATTR_DISCOVERED] = discovered
@@ -117,7 +132,13 @@ def async_listen_platform(
 
 
 @bind_hass
-def load_platform(hass, component, platform, discovered, hass_config):
+def load_platform(
+    hass: core.HomeAssistant,
+    component: str,
+    platform: str,
+    discovered: DiscoveryInfoType,
+    hass_config: ConfigType,
+) -> None:
     """Load a component and platform dynamically.
 
     Target components will be loaded and an EVENT_PLATFORM_DISCOVERED will be
@@ -129,12 +150,20 @@ def load_platform(hass, component, platform, discovered, hass_config):
     Use `listen_platform` to register a callback for these events.
     """
     hass.add_job(
-        async_load_platform(hass, component, platform, discovered, hass_config)
+        async_load_platform(  # type: ignore
+            hass, component, platform, discovered, hass_config
+        )
     )
 
 
 @bind_hass
-async def async_load_platform(hass, component, platform, discovered, hass_config):
+async def async_load_platform(
+    hass: core.HomeAssistant,
+    component: str,
+    platform: str,
+    discovered: DiscoveryInfoType,
+    hass_config: ConfigType,
+) -> None:
     """Load a component and platform dynamically.
 
     Target components will be loaded and an EVENT_PLATFORM_DISCOVERED will be
@@ -164,7 +193,7 @@ async def async_load_platform(hass, component, platform, discovered, hass_config
     if not setup_success:
         return
 
-    data = {
+    data: Dict[str, Any] = {
         ATTR_SERVICE: EVENT_LOAD_PLATFORM.format(component),
         ATTR_PLATFORM: platform,
     }
diff --git a/homeassistant/helpers/entity.py b/homeassistant/helpers/entity.py
index 7a3e1e8d52a..738b49f4c54 100644
--- a/homeassistant/helpers/entity.py
+++ b/homeassistant/helpers/entity.py
@@ -35,7 +35,7 @@ from homeassistant.helpers.entity_registry import (
 from homeassistant.util import dt as dt_util, ensure_unique_string, slugify
 from homeassistant.util.async_ import run_callback_threadsafe
 
-# mypy: allow-untyped-defs, no-check-untyped-defs, no-warn-return-any
+# mypy: allow-untyped-defs, no-check-untyped-defs
 
 _LOGGER = logging.getLogger(__name__)
 SLOW_UPDATE_WARNING = 10
diff --git a/homeassistant/helpers/entity_component.py b/homeassistant/helpers/entity_component.py
index 76c2cb9889e..4c30457b62c 100644
--- a/homeassistant/helpers/entity_component.py
+++ b/homeassistant/helpers/entity_component.py
@@ -191,7 +191,7 @@ class EntityComponent:
 
         This method must be run in the event loop.
         """
-        return await service.async_extract_entities(  # type: ignore
+        return await service.async_extract_entities(
             self.hass, self.entities, service_call, expand_group
         )
 
diff --git a/homeassistant/helpers/service.py b/homeassistant/helpers/service.py
index 7a352b4e8d1..77c436d212e 100644
--- a/homeassistant/helpers/service.py
+++ b/homeassistant/helpers/service.py
@@ -2,7 +2,7 @@
 import asyncio
 from functools import partial, wraps
 import logging
-from typing import Callable
+from typing import Any, Callable, Dict, Iterable, List, Optional, Set, Tuple
 
 import voluptuous as vol
 
@@ -22,9 +22,10 @@ from homeassistant.exceptions import (
     Unauthorized,
     UnknownUser,
 )
-from homeassistant.helpers import template, typing
+from homeassistant.helpers import template
 import homeassistant.helpers.config_validation as cv
-from homeassistant.helpers.typing import HomeAssistantType
+from homeassistant.helpers.entity import Entity
+from homeassistant.helpers.typing import ConfigType, HomeAssistantType, TemplateVarsType
 from homeassistant.loader import async_get_integration, bind_hass
 from homeassistant.util.yaml import load_yaml
 from homeassistant.util.yaml.loader import JSON_TYPE
@@ -42,8 +43,12 @@ SERVICE_DESCRIPTION_CACHE = "service_description_cache"
 
 @bind_hass
 def call_from_config(
-    hass, config, blocking=False, variables=None, validate_config=True
-):
+    hass: HomeAssistantType,
+    config: ConfigType,
+    blocking: bool = False,
+    variables: TemplateVarsType = None,
+    validate_config: bool = True,
+) -> None:
     """Call a service based on a config hash."""
     asyncio.run_coroutine_threadsafe(
         async_call_from_config(hass, config, blocking, variables, validate_config),
@@ -53,8 +58,13 @@ def call_from_config(
 
 @bind_hass
 async def async_call_from_config(
-    hass, config, blocking=False, variables=None, validate_config=True, context=None
-):
+    hass: HomeAssistantType,
+    config: ConfigType,
+    blocking: bool = False,
+    variables: TemplateVarsType = None,
+    validate_config: bool = True,
+    context: Optional[ha.Context] = None,
+) -> None:
     """Call a service based on a config hash."""
     try:
         parms = async_prepare_call_from_config(hass, config, variables, validate_config)
@@ -68,7 +78,12 @@ async def async_call_from_config(
 
 @ha.callback
 @bind_hass
-def async_prepare_call_from_config(hass, config, variables=None, validate_config=False):
+def async_prepare_call_from_config(
+    hass: HomeAssistantType,
+    config: ConfigType,
+    variables: TemplateVarsType = None,
+    validate_config: bool = False,
+) -> Tuple[str, str, Dict[str, Any]]:
     """Prepare to call a service based on a config hash."""
     if validate_config:
         try:
@@ -113,7 +128,9 @@ def async_prepare_call_from_config(hass, config, variables=None, validate_config
 
 
 @bind_hass
-def extract_entity_ids(hass, service_call, expand_group=True):
+def extract_entity_ids(
+    hass: HomeAssistantType, service_call: ha.ServiceCall, expand_group: bool = True
+) -> Set[str]:
     """Extract a list of entity ids from a service call.
 
     Will convert group entity ids to the entity ids it represents.
@@ -124,7 +141,12 @@ def extract_entity_ids(hass, service_call, expand_group=True):
 
 
 @bind_hass
-async def async_extract_entities(hass, entities, service_call, expand_group=True):
+async def async_extract_entities(
+    hass: HomeAssistantType,
+    entities: Iterable[Entity],
+    service_call: ha.ServiceCall,
+    expand_group: bool = True,
+) -> List[Entity]:
     """Extract a list of entity objects from a service call.
 
     Will convert group entity ids to the entity ids it represents.
@@ -158,7 +180,9 @@ async def async_extract_entities(hass, entities, service_call, expand_group=True
 
 
 @bind_hass
-async def async_extract_entity_ids(hass, service_call, expand_group=True):
+async def async_extract_entity_ids(
+    hass: HomeAssistantType, service_call: ha.ServiceCall, expand_group: bool = True
+) -> Set[str]:
     """Extract a list of entity ids from a service call.
 
     Will convert group entity ids to the entity ids it represents.
@@ -166,7 +190,7 @@ async def async_extract_entity_ids(hass, service_call, expand_group=True):
     entity_ids = service_call.data.get(ATTR_ENTITY_ID)
     area_ids = service_call.data.get(ATTR_AREA_ID)
 
-    extracted = set()
+    extracted: Set[str] = set()
 
     if entity_ids in (None, ENTITY_MATCH_NONE) and area_ids in (
         None,
@@ -226,7 +250,9 @@ async def _load_services_file(hass: HomeAssistantType, domain: str) -> JSON_TYPE
 
 
 @bind_hass
-async def async_get_all_descriptions(hass):
+async def async_get_all_descriptions(
+    hass: HomeAssistantType,
+) -> Dict[str, Dict[str, Any]]:
     """Return descriptions (i.e. user documentation) for all service calls."""
     descriptions_cache = hass.data.setdefault(SERVICE_DESCRIPTION_CACHE, {})
     format_cache_key = "{}.{}".format
@@ -253,7 +279,7 @@ async def async_get_all_descriptions(hass):
             loaded[domain] = content
 
     # Build response
-    descriptions = {}
+    descriptions: Dict[str, Dict[str, Any]] = {}
     for domain in services:
         descriptions[domain] = {}
 
@@ -281,7 +307,9 @@ async def async_get_all_descriptions(hass):
 
 @ha.callback
 @bind_hass
-def async_set_service_schema(hass, domain, service, schema):
+def async_set_service_schema(
+    hass: HomeAssistantType, domain: str, service: str, schema: Dict[str, Any]
+) -> None:
     """Register a description for a service."""
     hass.data.setdefault(SERVICE_DESCRIPTION_CACHE, {})
 
@@ -454,7 +482,7 @@ async def _handle_entity_call(hass, entity, func, data, context):
 @bind_hass
 @ha.callback
 def async_register_admin_service(
-    hass: typing.HomeAssistantType,
+    hass: HomeAssistantType,
     domain: str,
     service: str,
     service_func: Callable,
diff --git a/homeassistant/helpers/template.py b/homeassistant/helpers/template.py
index b6c59604b74..06bbf10a8ea 100644
--- a/homeassistant/helpers/template.py
+++ b/homeassistant/helpers/template.py
@@ -51,7 +51,7 @@ _RE_JINJA_DELIMITERS = re.compile(r"\{%|\{\{")
 
 
 @bind_hass
-def attach(hass, obj):
+def attach(hass: HomeAssistantType, obj: Any) -> None:
     """Recursively attach hass to all template instances in list and dict."""
     if isinstance(obj, list):
         for child in obj:
@@ -63,7 +63,7 @@ def attach(hass, obj):
         obj.hass = hass
 
 
-def render_complex(value, variables=None):
+def render_complex(value: Any, variables: TemplateVarsType = None) -> Any:
     """Recursive template creator helper function."""
     if isinstance(value, list):
         return [render_complex(item, variables) for item in value]
@@ -307,11 +307,11 @@ class Template:
             and self.hass == other.hass
         )
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         """Hash code for template."""
         return hash(self.template)
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         """Representation of Template."""
         return 'Template("' + self.template + '")'
 
@@ -333,7 +333,7 @@ class AllStates:
             raise TemplateError(f"Invalid domain name '{name}'")
         return DomainStates(self._hass, name)
 
-    def _collect_all(self):
+    def _collect_all(self) -> None:
         render_info = self._hass.data.get(_RENDER_INFO)
         if render_info is not None:
             # pylint: disable=protected-access
@@ -349,7 +349,7 @@ class AllStates:
             )
         )
 
-    def __len__(self):
+    def __len__(self) -> int:
         """Return number of states."""
         self._collect_all()
         return len(self._hass.states.async_entity_ids())
@@ -359,7 +359,7 @@ class AllStates:
         state = _get_state(self._hass, entity_id)
         return STATE_UNKNOWN if state is None else state.state
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         """Representation of All States."""
         return "<template AllStates>"
 
@@ -455,19 +455,21 @@ class TemplateState(State):
         return f"<template {rep[1:]}"
 
 
-def _collect_state(hass, entity_id):
+def _collect_state(hass: HomeAssistantType, entity_id: str) -> None:
     entity_collect = hass.data.get(_RENDER_INFO)
     if entity_collect is not None:
         # pylint: disable=protected-access
         entity_collect._entities.append(entity_id)
 
 
-def _wrap_state(hass, state):
+def _wrap_state(
+    hass: HomeAssistantType, state: Optional[State]
+) -> Optional[TemplateState]:
     """Wrap a state."""
     return None if state is None else TemplateState(hass, state)
 
 
-def _get_state(hass, entity_id):
+def _get_state(hass: HomeAssistantType, entity_id: str) -> Optional[TemplateState]:
     state = hass.states.get(entity_id)
     if state is None:
         # Only need to collect if none, if not none collect first actual
@@ -477,7 +479,9 @@ def _get_state(hass, entity_id):
     return _wrap_state(hass, state)
 
 
-def _resolve_state(hass, entity_id_or_state):
+def _resolve_state(
+    hass: HomeAssistantType, entity_id_or_state: Any
+) -> Union[State, TemplateState, None]:
     """Return state or entity_id if given."""
     if isinstance(entity_id_or_state, State):
         return entity_id_or_state
diff --git a/homeassistant/util/async_.py b/homeassistant/util/async_.py
index 5785759d591..0b48e2159c0 100644
--- a/homeassistant/util/async_.py
+++ b/homeassistant/util/async_.py
@@ -6,10 +6,12 @@ import functools
 import logging
 import threading
 from traceback import extract_stack
-from typing import Any, Callable, Coroutine
+from typing import Any, Callable, Coroutine, TypeVar
 
 _LOGGER = logging.getLogger(__name__)
 
+T = TypeVar("T")
+
 
 def fire_coroutine_threadsafe(coro: Coroutine, loop: AbstractEventLoop) -> None:
     """Submit a coroutine object to a given event loop.
@@ -33,8 +35,8 @@ def fire_coroutine_threadsafe(coro: Coroutine, loop: AbstractEventLoop) -> None:
 
 
 def run_callback_threadsafe(
-    loop: AbstractEventLoop, callback: Callable, *args: Any
-) -> concurrent.futures.Future:
+    loop: AbstractEventLoop, callback: Callable[..., T], *args: Any
+) -> "concurrent.futures.Future[T]":
     """Submit a callback object to a given event loop.
 
     Return a concurrent.futures.Future to access the result.