diff --git a/doc/whats_new/v0.21.rst b/doc/whats_new/v0.21.rst
index db4aa1b3250a3..a0334a4b36c4b 100644
--- a/doc/whats_new/v0.21.rst
+++ b/doc/whats_new/v0.21.rst
@@ -371,6 +371,11 @@ Support for Python 3.4 and below has been officially dropped.
   :func:`~model_selection.validation_curve` only the latter is required.
   :issue:`12613` and :issue:`12669` by :user:`Marc Torrellas <marctorrellas>`.
 
+- |Enhancement| Some :term:`CV splitter` classes and
+  `model_selection.train_test_split` now raise ``ValueError`` when the
+  resulting train set is empty. :issue:`12861` by :user:`Nicolas Hug
+  <NicolasHug>`.
+
 - |Fix| Fixed a bug where :class:`model_selection.StratifiedKFold`
   shuffles each class's samples with the same ``random_state``,
   making ``shuffle=True`` ineffective.
diff --git a/sklearn/model_selection/_split.py b/sklearn/model_selection/_split.py
index a3df4460cd261..fd6d5eb9c83e8 100644
--- a/sklearn/model_selection/_split.py
+++ b/sklearn/model_selection/_split.py
@@ -162,7 +162,13 @@ class LeaveOneOut(BaseCrossValidator):
     """
 
     def _iter_test_indices(self, X, y=None, groups=None):
-        return range(_num_samples(X))
+        n_samples = _num_samples(X)
+        if n_samples <= 1:
+            raise ValueError(
+                'Cannot perform LeaveOneOut with n_samples={}.'.format(
+                    n_samples)
+            )
+        return range(n_samples)
 
     def get_n_splits(self, X, y=None, groups=None):
         """Returns the number of splitting iterations in the cross-validator
@@ -209,7 +215,8 @@ class LeavePOut(BaseCrossValidator):
     Parameters
     ----------
     p : int
-        Size of the test sets.
+        Size of the test sets. Must be strictly greater than the number of
+        samples.
 
     Examples
     --------
@@ -238,7 +245,13 @@ def __init__(self, p):
         self.p = p
 
     def _iter_test_indices(self, X, y=None, groups=None):
-        for combination in combinations(range(_num_samples(X)), self.p):
+        n_samples = _num_samples(X)
+        if n_samples <= self.p:
+            raise ValueError(
+                'p={} must be strictly less than the number of '
+                'samples={}'.format(self.p, n_samples)
+            )
+        for combination in combinations(range(n_samples), self.p):
             yield np.array(combination)
 
     def get_n_splits(self, X, y=None, groups=None):
@@ -1862,7 +1875,17 @@ def _validate_shuffle_split(n_samples, test_size, train_size):
                          'samples %d. Reduce test_size and/or '
                          'train_size.' % (n_train + n_test, n_samples))
 
-    return int(n_train), int(n_test)
+    n_train, n_test = int(n_train), int(n_test)
+
+    if n_train == 0:
+        raise ValueError(
+            'With n_samples={}, test_size={} and train_size={}, the '
+            'resulting train set will be empty. Adjust any of the '
+            'aforementioned parameters.'.format(n_samples, test_size,
+                                                train_size)
+        )
+
+    return n_train, n_test
 
 
 class PredefinedSplit(BaseCrossValidator):
diff --git a/sklearn/model_selection/tests/test_split.py b/sklearn/model_selection/tests/test_split.py
index bdf466b92a7b6..e909bc791b489 100644
--- a/sklearn/model_selection/tests/test_split.py
+++ b/sklearn/model_selection/tests/test_split.py
@@ -1488,3 +1488,51 @@ def __repr__(self):
             return _build_repr(self)
 
     assert_equal(repr(MockSplitter(5, 6)), "MockSplitter(a=5, b=6, c=None)")
+
+
+@pytest.mark.parametrize('CVSplitter', (ShuffleSplit, GroupShuffleSplit,
+                                        StratifiedShuffleSplit))
+def test_shuffle_split_empty_trainset(CVSplitter):
+    cv = CVSplitter(test_size=.99)
+    X, y = [[1]], [0]  # 1 sample
+    with pytest.raises(
+            ValueError,
+            match='With n_samples=1, test_size=0.99 and train_size=None, '
+            'the resulting train set will be empty'):
+        next(cv.split(X, y, groups=[1]))
+
+
+def test_train_test_split_empty_trainset():
+    X, = [[1]]  # 1 sample
+    with pytest.raises(
+            ValueError,
+            match='With n_samples=1, test_size=0.99 and train_size=None, '
+            'the resulting train set will be empty'):
+        train_test_split(X, test_size=.99)
+
+    X = [[1], [1], [1]]  # 3 samples, ask for more than 2 thirds
+    with pytest.raises(
+            ValueError,
+            match='With n_samples=3, test_size=0.67 and train_size=None, '
+            'the resulting train set will be empty'):
+        train_test_split(X, test_size=.67)
+
+
+def test_leave_one_out_empty_trainset():
+    # LeaveOneGroup out expect at least 2 groups so no need to check
+    cv = LeaveOneOut()
+    X, y = [[1]], [0]  # 1 sample
+    with pytest.raises(
+            ValueError,
+            match='Cannot perform LeaveOneOut with n_samples=1'):
+        next(cv.split(X, y))
+
+
+def test_leave_p_out_empty_trainset():
+    # No need to check LeavePGroupsOut
+    cv = LeavePOut(p=2)
+    X, y = [[1], [2]], [0, 3]  # 2 samples
+    with pytest.raises(
+            ValueError,
+            match='p=2 must be strictly less than the number of samples=2'):
+        next(cv.split(X, y, groups=[1, 2]))