diff --git a/jedi/cache.py b/jedi/cache.py
index 29ed979f..1ff45201 100644
--- a/jedi/cache.py
+++ b/jedi/cache.py
@@ -13,14 +13,15 @@ these variables are being cleaned after every API usage.
 """
 import time
 from functools import wraps
+from typing import Any, Dict, Tuple
 
 from jedi import settings
 from parso.cache import parser_cache
 
-_time_caches = {}
+_time_caches: Dict[str, Dict[Any, Tuple[float, Any]]] = {}
 
 
-def clear_time_caches(delete_all=False):
+def clear_time_caches(delete_all: bool = False) -> None:
     """ Jedi caches many things, that should be completed after each completion
     finishes.
 
diff --git a/jedi/inference/filters.py b/jedi/inference/filters.py
index 6551cebc..35692169 100644
--- a/jedi/inference/filters.py
+++ b/jedi/inference/filters.py
@@ -3,9 +3,11 @@ Filters are objects that you can use to filter names in different scopes. They
 are needed for name resolution.
 """
 from abc import abstractmethod
+from typing import List, MutableMapping
 import weakref
 
 from parso.tree import search_ancestor
+from parso.python.tree import Name, UsedNamesMapping
 
 from jedi.inference import flow_analysis
 from jedi.inference.base_value import ValueSet, ValueWrapper, \
@@ -15,6 +17,7 @@ from jedi.inference.utils import to_list
 from jedi.inference.names import TreeNameDefinition, ParamName, \
     AnonymousParamName, AbstractNameDefinition
 
+_definition_name_cache: MutableMapping[UsedNamesMapping, List[Name]]
 _definition_name_cache = weakref.WeakKeyDictionary()
 
 
diff --git a/jedi/inference/flow_analysis.py b/jedi/inference/flow_analysis.py
index 184f367f..be67f23c 100644
--- a/jedi/inference/flow_analysis.py
+++ b/jedi/inference/flow_analysis.py
@@ -1,12 +1,14 @@
+from typing import Dict, Optional
+
 from jedi.parser_utils import get_flow_branch_keyword, is_scope, get_parent_scope
 from jedi.inference.recursion import execution_allowed
 from jedi.inference.helpers import is_big_annoying_library
 
 
 class Status(object):
-    lookup_table = {}
+    lookup_table: Dict[Optional[bool], 'Status'] = {}
 
-    def __init__(self, value, name):
+    def __init__(self, value: Optional[bool], name: str) -> None:
         self._value = value
         self._name = name
         Status.lookup_table[value] = self
diff --git a/jedi/inference/gradual/typeshed.py b/jedi/inference/gradual/typeshed.py
index e186bfc3..6295294d 100644
--- a/jedi/inference/gradual/typeshed.py
+++ b/jedi/inference/gradual/typeshed.py
@@ -2,6 +2,7 @@ import os
 import re
 from functools import wraps
 from collections import namedtuple
+from typing import Dict, Mapping, Tuple
 from pathlib import Path
 
 from jedi import settings
@@ -74,7 +75,7 @@ def _get_typeshed_directories(version_info):
             yield PathInfo(str(base_path.joinpath(check_version)), is_third_party)
 
 
-_version_cache = {}
+_version_cache: Dict[Tuple[int, int], Mapping[str, PathInfo]] = {}
 
 
 def _cache_stub_file_map(version_info):