diff --git a/README.md b/README.md
index a44d557f058b..f6f4e8c570e0 100644
--- a/README.md
+++ b/README.md
@@ -126,6 +126,8 @@ lightgbm-transform (feature transformation binding): https://github.com/microsof
 
 `postgresml` (LightGBM training and prediction in SQL, via a Postgres extension): https://github.com/postgresml/postgresml
 
+`vaex-ml` (Python DataFrame library with its own interface to LightGBM): https://github.com/vaexio/vaex
+
 Support
 -------
 
diff --git a/python-package/lightgbm/engine.py b/python-package/lightgbm/engine.py
index 60a4bc8d1d61..5c73838c0f85 100644
--- a/python-package/lightgbm/engine.py
+++ b/python-package/lightgbm/engine.py
@@ -658,13 +658,18 @@ def cv(
 
     Returns
     -------
-    eval_hist : dict
-        Evaluation history.
+    eval_results : dict
+        History of evaluation results of each metric.
         The dictionary has the following format:
-        {'metric1-mean': [values], 'metric1-stdv': [values],
-        'metric2-mean': [values], 'metric2-stdv': [values],
+        {'valid metric1-mean': [values], 'valid metric1-stdv': [values],
+        'valid metric2-mean': [values], 'valid metric2-stdv': [values],
         ...}.
         If ``return_cvbooster=True``, also returns trained boosters wrapped in a ``CVBooster`` object via ``cvbooster`` key.
+        If ``eval_train_metric=True``, also returns the train metric history.
+        In this case, the dictionary has the following format:
+        {'train metric1-mean': [values], 'valid metric1-mean': [values],
+        'train metric2-mean': [values], 'valid metric2-mean': [values],
+        ...}.
     """
     if not isinstance(train_set, Dataset):
         raise TypeError(f"cv() only accepts Dataset object, train_set has type '{type(train_set).__name__}'.")