diff --git a/doc/source/reference/frame.rst b/doc/source/reference/frame.rst
index 411eb3dbbedc8d..2eeb11a72df274 100644
--- a/doc/source/reference/frame.rst
+++ b/doc/source/reference/frame.rst
@@ -275,6 +275,19 @@ Time series-related
    DataFrame.tz_convert
    DataFrame.tz_localize
 
+.. _api.frame.metadata:
+
+Metadata
+~~~~~~~~
+
+:attr:`DataFrame.attrs` is a dictionary for storing global metadata for this DataFrame.
+
+.. autosummary::
+   :toctree: api/
+
+   DataFrame.attrs
+
+
 .. _api.dataframe.plotting:
 
 Plotting
diff --git a/doc/source/reference/series.rst b/doc/source/reference/series.rst
index bb53f45d96303d..a160893a97db2a 100644
--- a/doc/source/reference/series.rst
+++ b/doc/source/reference/series.rst
@@ -532,6 +532,19 @@ Sparse-dtype specific methods and attributes are provided under the
    Series.sparse.to_coo
 
 
+.. _api.series.metadata:
+
+Metadata
+~~~~~~~~
+
+:attr:`Series.attrs` is a dictionary for storing global metadata for this Series.
+
+.. autosummary::
+   :toctree: api/
+
+   Series.attrs
+
+
 Plotting
 --------
 ``Series.plot`` is both a callable method and a namespace attribute for
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index e1968e966d689f..dbbf630b692da4 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -8,12 +8,14 @@
 import re
 from textwrap import dedent
 from typing import (
+    TYPE_CHECKING,
     Any,
     Callable,
     Dict,
     FrozenSet,
     Hashable,
     List,
+    Mapping,
     Optional,
     Sequence,
     Set,
@@ -189,6 +191,12 @@ class NDFrame(PandasObject, SelectionMixin):
     _is_copy = None
     _data = None  # type: BlockManager
 
+    if TYPE_CHECKING:
+        # TODO(PY36): replace with _attrs : Dict[Hashable, Any]
+        # We need the TYPE_CHECKING, because _attrs is not a class attribute
+        # and Py35 doesn't support the new syntax.
+        _attrs = {}  # type: Dict[Hashable, Any]
+
     # ----------------------------------------------------------------------
     # Constructors
 
@@ -199,6 +207,7 @@ def __init__(
         copy: bool = False,
         dtype: Optional[Dtype] = None,
         allow_duplicate_labels: bool = True,
+        attrs: Optional[Mapping[Hashable, Any]] = None,
         fastpath: bool = False,
     ):
 
@@ -216,6 +225,11 @@ def __init__(
         object.__setattr__(self, "_data", data)
         object.__setattr__(self, "_item_cache", {})
         object.__setattr__(self, "allows_duplicate_labels", allow_duplicate_labels)
+        if attrs is None:
+            attrs = {}
+        else:
+            attrs = dict(attrs)
+        object.__setattr__(self, "_attrs", attrs)
 
     def _init_mgr(self, mgr, axes=None, dtype=None, copy=False):
         """ passed a manager and a axes dict """
@@ -252,6 +266,18 @@ def allows_duplicate_labels(self, value: bool):
 
         self._allows_duplicate_labels = value
 
+    def attrs(self) -> Dict[Hashable, Any]:
+        """
+        Dictionary of global attributes on this object.
+        """
+        if self._attrs is None:
+            self._attrs = {}
+        return self._attrs
+
+    @attrs.setter
+    def attrs(self, value: Mapping[Hashable, Any]) -> None:
+        self._attrs = dict(value)
+
     @property
     def is_copy(self):
         """
@@ -2048,7 +2074,13 @@ def to_dense(self):
 
     def __getstate__(self):
         meta = {k: getattr(self, k, None) for k in self._metadata}
-        return dict(_data=self._data, _typ=self._typ, _metadata=self._metadata, **meta)
+        return dict(
+            _data=self._data,
+            _typ=self._typ,
+            _metadata=self._metadata,
+            attrs=self.attrs,
+            **meta
+        )
 
     def __setstate__(self, state):
 
@@ -2057,6 +2089,8 @@ def __setstate__(self, state):
         elif isinstance(state, dict):
             typ = state.get("_typ")
             if typ is not None:
+                attrs = state.get("_attrs", {})
+                object.__setattr__(self, "_attrs", attrs)
 
                 # set in the order of internal names
                 # to avoid definitional recursion
@@ -5255,6 +5289,9 @@ def finalize_name(objs):
 
         # import pdb; pdb.set_trace()
         if isinstance(other, NDFrame):
+            for name in other.attrs:
+                self.attrs[name] = other.attrs[name]
+            # For subclasses using _metadata.
             for name in self._metadata:
                 if name == "name" and getattr(other, "ndim", None) == 1:
                     # Calling hasattr(other, 'name') is bad for DataFrames with
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 96f506b64d19d9..c9447677713a66 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -5,7 +5,7 @@
 from io import StringIO
 from shutil import get_terminal_size
 from textwrap import dedent
-from typing import Any, Callable
+from typing import Any, Callable, Hashable, List
 import warnings
 
 import numpy as np
@@ -29,7 +29,6 @@
     is_dict_like,
     is_extension_array_dtype,
     is_extension_type,
-    is_hashable,
     is_integer,
     is_iterator,
     is_list_like,
@@ -45,6 +44,7 @@
     ABCSeries,
     ABCSparseArray,
 )
+from pandas.core.dtypes.inference import is_hashable
 from pandas.core.dtypes.missing import (
     isna,
     na_value_for_dtype,
@@ -179,7 +179,7 @@ class Series(base.IndexOpsMixin, generic.NDFrame):
         introduces duplicates. See :ref:`duplictes.disallow` for more.
     """
 
-    _metadata = ["name", "allows_duplicate_labels"]
+    _metadata = []  # type: List[str]
     _accessors = {"dt", "cat", "str", "sparse"}
     _deprecations = (
         base.IndexOpsMixin._deprecations
@@ -472,19 +472,6 @@ def _update_inplace(self, result, **kwargs):
         # we want to call the generic version and not the IndexOpsMixin
         return generic.NDFrame._update_inplace(self, result, **kwargs)
 
-    @property
-    def name(self):
-        """
-        Return name of the Series.
-        """
-        return self._name
-
-    @name.setter
-    def name(self, value):
-        if value is not None and not is_hashable(value):
-            raise TypeError("Series.name must be a hashable type")
-        object.__setattr__(self, "_name", value)
-
     # ndarray compatibility
     @property
     def dtype(self):
@@ -500,6 +487,16 @@ def dtypes(self):
         """
         return self._data.dtype
 
+    @property
+    def name(self) -> Hashable:
+        return self.attrs.get("name", None)
+
+    @name.setter
+    def name(self, value: Hashable) -> None:
+        if not is_hashable(value):
+            raise TypeError("Series.name must be a hashable type")
+        self.attrs["name"] = value
+
     @property
     def ftype(self):
         """