diff --git a/mmcv/runner/hooks/eval.py b/mmcv/runner/hooks/eval.py
index 114406aee62..440372b52b0 100644
--- a/mmcv/runner/hooks/eval.py
+++ b/mmcv/runner/hooks/eval.py
@@ -11,11 +11,14 @@
 
 class EvalHook(Hook):
     """Non-Distributed evaluation hook.
+
     Notes:
         If new arguments are added for EvalHook, tools/test.py,
         tools/eval_metric.py may be effected.
+
     This hook will regularly perform evaluation in a given interval when
     performing in non-distributed environment.
+
     Args:
         dataloader (DataLoader): A PyTorch dataloader.
         start (int | None, optional): Evaluation starting epoch. It enables
@@ -32,8 +35,9 @@ class EvalHook(Hook):
             Options are the evaluation metrics to the test dataset. e.g.,
             ``bbox_mAP``, ``segm_mAP`` for bbox detection and instance
             segmentation. ``AR@100`` for proposal recall. If ``save_best`` is
-            ``auto``, the first key will be used. The interval of
-            ``CheckpointHook`` should device EvalHook. Default: None.
+            ``auto``, the first key of the returned ``OrderedDict`` result
+            will be used. The interval of ``CheckpointHook`` should device
+            ``EvalHook``. Default: None.
         rule (str | None, optional): Comparison rule for best score. If set to
             None, it will infer a reasonable rule. Keys such as 'acc', 'top'
             .etc will be inferred by 'greater' rule. Keys contain 'loss' will
@@ -78,7 +82,7 @@ def __init__(self,
         assert isinstance(save_best, str) or save_best is None
         self.save_best = save_best
         self.eval_kwargs = eval_kwargs
-        self.initial_epoch_flag = True
+        self.initial_flag = True
 
         if self.save_best is not None:
             self._init_rule(rule, self.save_best)
@@ -121,21 +125,21 @@ def before_train_iter(self, runner):
         """Evaluate the model only at the start of training by iteration."""
         if self.by_epoch:
             return
-        if not self.initial_epoch_flag:
+        if not self.initial_flag:
             return
         if self.start is not None and runner.iter >= self.start:
             self.after_train_iter(runner)
-        self.initial_epoch_flag = False
+        self.initial_flag = False
 
     def before_train_epoch(self, runner):
         """Evaluate the model only at the start of training by epoch."""
         if not self.by_epoch:
             return
-        if not self.initial_epoch_flag:
+        if not self.initial_flag:
             return
         if self.start is not None and runner.epoch >= self.start:
             self.after_train_epoch(runner)
-        self.initial_epoch_flag = False
+        self.initial_flag = False
 
     def after_train_iter(self, runner):
         """Called after every training iter to evaluate the results."""
@@ -178,7 +182,8 @@ def evaluation_flag(self, runner):
             # No evaluation if start is larger than the current time.
             return False
         else:
-            # Evaluation only at epochs 3, 5, 7... if start==3 and interval==2
+            # Evaluation only at epochs/iters 3, 5, 7...
+            # if start==3 and interval==2
             if (current + 1 - self.start) % self.interval:
                 return False
         return True
@@ -187,7 +192,7 @@ def _save_ckpt(self, runner, key_score):
         if self.by_epoch:
             current = f'epoch_{runner.epoch + 1}'
         else:
-            current = f'iter_{runner.epoch + 1}'
+            current = f'iter_{runner.iter + 1}'
 
         best_score = runner.meta['hook_msgs'].get(
             'best_score', self.init_value_map[self.rule])
@@ -226,8 +231,10 @@ def evaluate(self, runner, results):
 
 class DistEvalHook(EvalHook):
     """Distributed evaluation hook.
+
     This hook will regularly perform evaluation in a given interval when
     performing in distributed environment.
+
     Args:
         dataloader (DataLoader): A PyTorch dataloader.
         start (int | None, optional): Evaluation starting epoch. It enables
@@ -244,8 +251,9 @@ class DistEvalHook(EvalHook):
             Options are the evaluation metrics to the test dataset. e.g.,
             ``bbox_mAP``, ``segm_mAP`` for bbox detection and instance
             segmentation. ``AR@100`` for proposal recall. If ``save_best`` is
-            ``auto``, the first key will be used. The interval of
-            ``CheckpointHook`` should device EvalHook. Default: None.
+            ``auto``, the first key of the returned ``OrderedDict`` result
+            will be used. The interval of ``CheckpointHook`` should depend on
+            ``EvalHook``. Default: None.
         rule (str | None, optional): Comparison rule for best score. If set to
             None, it will infer a reasonable rule. Keys such as 'acc', 'top'
             .etc will be inferred by 'greater' rule. Keys contain 'loss' will