diff --git a/ignite/contrib/engines/common.py b/ignite/contrib/engines/common.py
index c8fed964993a..ed7169fd5b3c 100644
--- a/ignite/contrib/engines/common.py
+++ b/ignite/contrib/engines/common.py
@@ -1,10 +1,12 @@
 import numbers
 import warnings
-from collections.abc import Mapping, Sequence
 from functools import partial
+from typing import Any, Callable, Dict, Iterable, Mapping, Optional, Sequence, Union
 
 import torch
 import torch.nn as nn
+from torch.optim.lr_scheduler import _LRScheduler
+from torch.optim.optimizer import Optimizer
 from torch.utils.data.distributed import DistributedSampler
 
 import ignite.distributed as idist
@@ -20,29 +22,32 @@
     WandBLogger,
     global_step_from_engine,
 )
+from ignite.contrib.handlers.base_logger import BaseLogger
+from ignite.contrib.handlers.param_scheduler import ParamScheduler
 from ignite.contrib.metrics import GpuInfo
 from ignite.engine import Engine, Events
 from ignite.handlers import Checkpoint, DiskSaver, EarlyStopping, TerminateOnNan
+from ignite.handlers.checkpoint import BaseSaveHandler
 from ignite.metrics import RunningAverage
 
 
 def setup_common_training_handlers(
-    trainer,
-    train_sampler=None,
-    to_save=None,
-    save_every_iters=1000,
-    output_path=None,
-    lr_scheduler=None,
-    with_gpu_stats=False,
-    output_names=None,
-    with_pbars=True,
-    with_pbar_on_iters=True,
-    log_every_iters=100,
-    device=None,
-    stop_on_nan=True,
-    clear_cuda_cache=True,
-    save_handler=None,
-    **kwargs
+    trainer: Engine,
+    train_sampler: Optional[DistributedSampler] = None,
+    to_save: Optional[Mapping] = None,
+    save_every_iters: int = 1000,
+    output_path: Optional[str] = None,
+    lr_scheduler: Optional[Union[ParamScheduler, _LRScheduler]] = None,
+    with_gpu_stats: bool = False,
+    output_names: Optional[Iterable[str]] = None,
+    with_pbars: bool = True,
+    with_pbar_on_iters: bool = True,
+    log_every_iters: int = 100,
+    device: Optional[Union[str, torch.device]] = None,
+    stop_on_nan: bool = True,
+    clear_cuda_cache: bool = True,
+    save_handler: Optional[Union[Callable, BaseSaveHandler]] = None,
+    **kwargs: Any
 ):
     """Helper method to setup trainer with common handlers (it also supports distributed configuration):
         - :class:`~ignite.handlers.TerminateOnNan`
@@ -119,20 +124,20 @@ class to use to store ``to_save``. See :class:`~ignite.handlers.checkpoint.Check
 
 
 def _setup_common_training_handlers(
-    trainer,
-    to_save=None,
-    save_every_iters=1000,
-    output_path=None,
-    lr_scheduler=None,
-    with_gpu_stats=False,
-    output_names=None,
-    with_pbars=True,
-    with_pbar_on_iters=True,
-    log_every_iters=100,
-    stop_on_nan=True,
-    clear_cuda_cache=True,
-    save_handler=None,
-    **kwargs
+    trainer: Engine,
+    to_save: Optional[Mapping] = None,
+    save_every_iters: int = 1000,
+    output_path: Optional[str] = None,
+    lr_scheduler: Optional[Union[ParamScheduler, _LRScheduler]] = None,
+    with_gpu_stats: bool = False,
+    output_names: Optional[Iterable[str]] = None,
+    with_pbars: bool = True,
+    with_pbar_on_iters: bool = True,
+    log_every_iters: int = 100,
+    stop_on_nan: bool = True,
+    clear_cuda_cache: bool = True,
+    save_handler: Optional[Union[Callable, BaseSaveHandler]] = None,
+    **kwargs: Any
 ):
     if output_path is not None and save_handler is not None:
         raise ValueError(
@@ -200,21 +205,21 @@ def output_transform(x, index, name):
 
 
 def _setup_common_distrib_training_handlers(
-    trainer,
-    train_sampler=None,
-    to_save=None,
-    save_every_iters=1000,
-    output_path=None,
-    lr_scheduler=None,
-    with_gpu_stats=False,
-    output_names=None,
-    with_pbars=True,
-    with_pbar_on_iters=True,
-    log_every_iters=100,
-    stop_on_nan=True,
-    clear_cuda_cache=True,
-    save_handler=None,
-    **kwargs
+    trainer: Engine,
+    train_sampler: Optional[DistributedSampler] = None,
+    to_save: Optional[Mapping] = None,
+    save_every_iters: int = 1000,
+    output_path: Optional[str] = None,
+    lr_scheduler: Optional[Union[ParamScheduler, _LRScheduler]] = None,
+    with_gpu_stats: bool = False,
+    output_names: Optional[Iterable[str]] = None,
+    with_pbars: bool = True,
+    with_pbar_on_iters: bool = True,
+    log_every_iters: int = 100,
+    stop_on_nan: bool = True,
+    clear_cuda_cache: bool = True,
+    save_handler: Optional[Union[Callable, BaseSaveHandler]] = None,
+    **kwargs: Any
 ):
 
     _setup_common_training_handlers(
@@ -257,10 +262,14 @@ def setup_any_logging(logger, logger_module, trainer, optimizers, evaluators, lo
     )
 
 
-def _setup_logging(logger, trainer, optimizers, evaluators, log_every_iters):
+def _setup_logging(
+    logger: BaseLogger,
+    trainer: Engine,
+    optimizers: Union[Optimizer, Dict[str, Optimizer]],
+    evaluators: Union[Engine, Dict[str, Engine]],
+    log_every_iters: int,
+):
     if optimizers is not None:
-        from torch.optim.optimizer import Optimizer
-
         if not isinstance(optimizers, (Optimizer, Mapping)):
             raise TypeError("Argument optimizers should be either a single optimizer or a dictionary or optimizers")
 
@@ -298,7 +307,14 @@ def _setup_logging(logger, trainer, optimizers, evaluators, log_every_iters):
             )
 
 
-def setup_tb_logging(output_path, trainer, optimizers=None, evaluators=None, log_every_iters=100, **kwargs):
+def setup_tb_logging(
+    output_path: str,
+    trainer: Engine,
+    optimizers: Optional[Union[Optimizer, Dict[str, Optimizer]]] = None,
+    evaluators: Optional[Union[Engine, Dict[str, Engine]]] = None,
+    log_every_iters: int = 100,
+    **kwargs: Any
+):
     """Method to setup TensorBoard logging on trainer and a list of evaluators. Logged metrics are:
         - Training metrics, e.g. running average loss values
         - Learning rate(s)
@@ -323,7 +339,13 @@ def setup_tb_logging(output_path, trainer, optimizers=None, evaluators=None, log
     return logger
 
 
-def setup_visdom_logging(trainer, optimizers=None, evaluators=None, log_every_iters=100, **kwargs):
+def setup_visdom_logging(
+    trainer: Engine,
+    optimizers: Optional[Union[Optimizer, Dict[str, Optimizer]]] = None,
+    evaluators: Optional[Union[Engine, Dict[str, Engine]]] = None,
+    log_every_iters: int = 100,
+    **kwargs: Any
+):
     """Method to setup Visdom logging on trainer and a list of evaluators. Logged metrics are:
         - Training metrics, e.g. running average loss values
         - Learning rate(s)
@@ -347,7 +369,13 @@ def setup_visdom_logging(trainer, optimizers=None, evaluators=None, log_every_it
     return logger
 
 
-def setup_mlflow_logging(trainer, optimizers=None, evaluators=None, log_every_iters=100, **kwargs):
+def setup_mlflow_logging(
+    trainer: Engine,
+    optimizers: Optional[Union[Optimizer, Dict[str, Optimizer]]] = None,
+    evaluators: Optional[Union[Engine, Dict[str, Engine]]] = None,
+    log_every_iters: int = 100,
+    **kwargs: Any
+):
     """Method to setup MLflow logging on trainer and a list of evaluators. Logged metrics are:
         - Training metrics, e.g. running average loss values
         - Learning rate(s)
@@ -371,7 +399,13 @@ def setup_mlflow_logging(trainer, optimizers=None, evaluators=None, log_every_it
     return logger
 
 
-def setup_neptune_logging(trainer, optimizers=None, evaluators=None, log_every_iters=100, **kwargs):
+def setup_neptune_logging(
+    trainer: Engine,
+    optimizers: Optional[Union[Optimizer, Dict[str, Optimizer]]] = None,
+    evaluators: Optional[Union[Engine, Dict[str, Engine]]] = None,
+    log_every_iters: int = 100,
+    **kwargs: Any
+):
     """Method to setup Neptune logging on trainer and a list of evaluators. Logged metrics are:
         - Training metrics, e.g. running average loss values
         - Learning rate(s)
@@ -395,7 +429,13 @@ def setup_neptune_logging(trainer, optimizers=None, evaluators=None, log_every_i
     return logger
 
 
-def setup_wandb_logging(trainer, optimizers=None, evaluators=None, log_every_iters=100, **kwargs):
+def setup_wandb_logging(
+    trainer: Engine,
+    optimizers: Optional[Union[Optimizer, Dict[str, Optimizer]]] = None,
+    evaluators: Optional[Union[Engine, Dict[str, Engine]]] = None,
+    log_every_iters: int = 100,
+    **kwargs: Any
+):
     """Method to setup WandB logging on trainer and a list of evaluators. Logged metrics are:
         - Training metrics, e.g. running average loss values
         - Learning rate(s)
@@ -419,7 +459,13 @@ def setup_wandb_logging(trainer, optimizers=None, evaluators=None, log_every_ite
     return logger
 
 
-def setup_plx_logging(trainer, optimizers=None, evaluators=None, log_every_iters=100, **kwargs):
+def setup_plx_logging(
+    trainer: Engine,
+    optimizers: Optional[Union[Optimizer, Dict[str, Optimizer]]] = None,
+    evaluators: Optional[Union[Engine, Dict[str, Engine]]] = None,
+    log_every_iters: int = 100,
+    **kwargs: Any
+):
     """Method to setup Polyaxon logging on trainer and a list of evaluators. Logged metrics are:
         - Training metrics, e.g. running average loss values
         - Learning rate(s)
@@ -443,7 +489,13 @@ def setup_plx_logging(trainer, optimizers=None, evaluators=None, log_every_iters
     return logger
 
 
-def setup_trains_logging(trainer, optimizers=None, evaluators=None, log_every_iters=100, **kwargs):
+def setup_trains_logging(
+    trainer: Engine,
+    optimizers: Optional[Union[Optimizer, Dict[str, Optimizer]]] = None,
+    evaluators: Optional[Union[Engine, Dict[str, Engine]]] = None,
+    log_every_iters: int = 100,
+    **kwargs: Any
+):
     """Method to setup Trains logging on trainer and a list of evaluators. Logged metrics are:
         - Training metrics, e.g. running average loss values
         - Learning rate(s)
@@ -467,8 +519,8 @@ def setup_trains_logging(trainer, optimizers=None, evaluators=None, log_every_it
     return logger
 
 
-def get_default_score_fn(metric_name):
-    def wrapper(engine):
+def get_default_score_fn(metric_name: str):
+    def wrapper(engine: Engine):
         score = engine.state.metrics[metric_name]
         return score
 
@@ -476,7 +528,14 @@ def wrapper(engine):
 
 
 def gen_save_best_models_by_val_score(
-    save_handler, evaluator, models, metric_name, n_saved=3, trainer=None, tag="val", **kwargs
+    save_handler: Union[Callable, BaseSaveHandler],
+    evaluator: Engine,
+    models: Union[torch.nn.Module, Dict[str, torch.nn.Module]],
+    metric_name: str,
+    n_saved: int = 3,
+    trainer: Optional[Engine] = None,
+    tag: str = "val",
+    **kwargs: Any
 ):
     """Method adds a handler to ``evaluator`` to save ``n_saved`` of best models based on the metric
     (named by ``metric_name``) provided by ``evaluator`` (i.e. ``evaluator.state.metrics[metric_name]``).
@@ -521,15 +580,20 @@ def gen_save_best_models_by_val_score(
         score_function=get_default_score_fn(metric_name),
         **kwargs,
     )
-    evaluator.add_event_handler(
-        Events.COMPLETED, best_model_handler,
-    )
+    evaluator.add_event_handler(Events.COMPLETED, best_model_handler)
 
     return best_model_handler
 
 
 def save_best_model_by_val_score(
-    output_path, evaluator, model, metric_name, n_saved=3, trainer=None, tag="val", **kwargs
+    output_path: str,
+    evaluator: Engine,
+    model: torch.nn.Module,
+    metric_name: str,
+    n_saved: int = 3,
+    trainer: Optional[Engine] = None,
+    tag: str = "val",
+    **kwargs: Any
 ):
     """Method adds a handler to ``evaluator`` to save on a disk ``n_saved`` of best models based on the metric
     (named by ``metric_name``) provided by ``evaluator`` (i.e. ``evaluator.state.metrics[metric_name]``).
@@ -561,7 +625,7 @@ def save_best_model_by_val_score(
     )
 
 
-def add_early_stopping_by_val_score(patience, evaluator, trainer, metric_name):
+def add_early_stopping_by_val_score(patience: int, evaluator: Engine, trainer: Engine, metric_name: str):
     """Method setups early stopping handler based on the score (named by `metric_name`) provided by `evaluator`.
     Metric value should increase in order to keep training and not early stop.
 
diff --git a/ignite/contrib/engines/tbptt.py b/ignite/contrib/engines/tbptt.py
index f959673c2b0c..d6ef72b26e43 100644
--- a/ignite/contrib/engines/tbptt.py
+++ b/ignite/contrib/engines/tbptt.py
@@ -1,6 +1,9 @@
 # coding: utf-8
+from typing import Callable, Mapping, Optional, Sequence, Union
 
 import torch
+import torch.nn as nn
+from torch.optim.optimizer import Optimizer
 
 from ignite.engine import Engine, EventEnum, _prepare_batch
 from ignite.utils import apply_to_tensor
@@ -17,7 +20,7 @@ class Tbptt_Events(EventEnum):
     TIME_ITERATION_COMPLETED = "time_iteration_completed"
 
 
-def _detach_hidden(hidden):
+def _detach_hidden(hidden: Union[torch.Tensor, Sequence, Mapping, str, bytes]):
     """Cut backpropagation graph.
 
     Auxillary function to cut the backpropagation graph by detaching the hidden
@@ -27,7 +30,14 @@ def _detach_hidden(hidden):
 
 
 def create_supervised_tbptt_trainer(
-    model, optimizer, loss_fn, tbtt_step, dim=0, device=None, non_blocking=False, prepare_batch=_prepare_batch
+    model: nn.Module,
+    optimizer: Optimizer,
+    loss_fn: nn.Module,
+    tbtt_step: int,
+    dim: int = 0,
+    device: Optional[str] = None,
+    non_blocking: bool = False,
+    prepare_batch: Callable = _prepare_batch,
 ):
     """Create a trainer for truncated backprop through time supervised models.
 
@@ -73,7 +83,7 @@ def create_supervised_tbptt_trainer(
 
     """
 
-    def _update(engine, batch):
+    def _update(engine: Engine, batch: Sequence[torch.Tensor]):
         loss_list = []
         hidden = None