diff --git a/lib/interval/interval.ex b/lib/interval/interval.ex
index a8ead465..76a15482 100644
--- a/lib/interval/interval.ex
+++ b/lib/interval/interval.ex
@@ -382,6 +382,42 @@ defmodule Timex.Interval do
   def max(%__MODULE__{until: until, right_open: false}), do: until
   def max(%__MODULE__{until: until}), do: Timex.shift(until, microseconds: -1)
 
+  @doc """
+  Returns an Interval of the overlap between two intervals.
+  """
+  @spec overlap(__MODULE__.t(), __MODULE__.t()) :: t() | {:error, :no_overlap_interval}
+  def overlap(%__MODULE__{} = a, %__MODULE__{} = b) do
+    {from, left_open} = start_of_overlap(a, b)
+    {until, right_open} = end_of_overlap(a, b)
+
+    case new(from: from, until: until, left_open: left_open, right_open: right_open) do
+      {:error, _} -> {:error, :no_overlap_interval}
+      interval -> interval
+    end
+  end
+
+  @doc """
+  Take the later start time of the two overlapping intervals,
+  and the left_open value of that interval.
+  """
+  defp start_of_overlap(%__MODULE__{} = a, %__MODULE__{} = b) do
+    case Timex.before?(a.from, b.from) do
+      true -> {b.from, b.left_open}
+      false -> {a.from, a.left_open}
+    end
+  end
+
+  @doc """
+  Take the earlier end time of the 2 overlapping intervals,
+  and the right_open value of that interval.
+  """
+  defp end_of_overlap(%__MODULE__{} = a, %__MODULE__{} = b) do
+    case Timex.before?(a.until, b.until) do
+      true -> {a.until, a.right_open}
+      false -> {b.until, b.right_open}
+    end
+  end
+
   defimpl Enumerable do
     alias Timex.Interval
 
diff --git a/test/interval_test.exs b/test/interval_test.exs
index 1a1f8f71..1de4a765 100644
--- a/test/interval_test.exs
+++ b/test/interval_test.exs
@@ -196,6 +196,99 @@ defmodule IntervalTests do
     end
   end
 
+  describe "overlap" do
+    test "non-overlapping intervals" do
+      a = Interval.new(from: ~N[2017-01-02 15:00:00], until: ~N[2017-01-02 15:15:00])
+      b = Interval.new(from: ~N[2017-01-02 15:30:00], until: ~N[2017-01-02 15:45:00])
+
+      assert {:error, _} = Interval.overlap(a, b)
+    end
+
+    test "non-overlapping back-to-back intervals" do
+      a = Interval.new(from: ~N[2017-01-02 15:00:00], until: ~N[2017-01-02 15:15:00], right_open: true)
+      b = Interval.new(from: ~N[2017-01-02 15:15:00], until: ~N[2017-01-02 15:30:00])
+
+      assert {:error, _} = Interval.overlap(a, b)
+    end
+
+    test "overlapping at single instant with closed bounds" do
+      a = Interval.new(from: ~N[2017-01-02 15:00:00], until: ~N[2017-01-02 15:15:00], right_open: false)
+      b = Interval.new(from: ~N[2017-01-02 15:15:00], until: ~N[2017-01-02 15:30:00], left_open: false)
+
+      assert {:error, _} = Interval.overlap(a, b)
+    end
+
+    test "first subset of second" do
+      a = Interval.new(from: ~N[2017-01-02 15:00:00], until: ~N[2017-01-02 15:45:00])
+      b = Interval.new(from: ~N[2017-01-02 15:20:00], until: ~N[2017-01-02 15:30:00])
+
+      assert Interval.new(from: ~N[2017-01-02 15:20:00], until: ~N[2017-01-02 15:30:00]) == Interval.overlap(a, b)
+    end
+
+    test "partially overlapping" do
+      a = Interval.new(from: ~N[2017-01-02 15:00:00], until: ~N[2017-01-02 15:15:00])
+      b = Interval.new(from: ~N[2017-01-02 15:10:00], until: ~N[2017-01-02 15:30:00])
+
+      assert Interval.new(from: ~N[2017-01-02 15:10:00], until: ~N[2017-01-02 15:15:00]) == Interval.overlap(a, b)
+    end
+
+    test "overlapping across hours" do
+      a = Interval.new(from: ~N[2017-01-02 14:50:00], until: ~N[2017-01-02 15:15:00])
+      b = Interval.new(from: ~N[2017-01-02 14:55:00], until: ~N[2017-01-02 15:30:00])
+      
+      assert Interval.new(from: ~N[2017-01-02 14:55:00], until: ~N[2017-01-02 15:15:00]) == Interval.overlap(a, b)
+    end
+
+    test "overlapping across days" do
+      a = Interval.new(from: ~N[2017-01-15 23:40:00], until: ~N[2017-01-16 00:10:00])
+      b = Interval.new(from: ~N[2017-01-15 23:50:00], until: ~N[2017-01-16 00:20:00])
+
+      assert Interval.new(from: ~N[2017-01-15 23:50:00], until: ~N[2017-01-16 00:10:00]) == Interval.overlap(a, b)
+    end
+
+    test "overlapping across months" do
+      a = Interval.new(from: ~N[2017-06-30 23:40:00], until: ~N[2017-07-01 00:10:00])
+      b = Interval.new(from: ~N[2017-06-30 23:50:00], until: ~N[2017-07-01 00:20:00])
+
+      assert Interval.new(from: ~N[2017-06-30 23:50:00], until: ~N[2017-07-01 00:10:00]) == Interval.overlap(a, b)
+    end
+
+    test "overlapping across years" do
+      a = Interval.new(from: ~N[2016-12-31 23:30:00], until: ~N[2017-01-01 00:30:00])
+      b = Interval.new(from: ~N[2016-12-31 23:45:00], until: ~N[2017-01-01 00:15:00])
+
+      assert Interval.new(from: ~N[2016-12-31 23:45:00], until: ~N[2017-01-01 00:15:00]) == Interval.overlap(a, b)
+    end
+
+    test "shared from/until with different openness" do
+      a = Interval.new(from: ~N[2017-01-02 15:00:00], until: ~N[2017-01-02 15:15:00], left_open: true, right_open: false)
+      b = Interval.new(from: ~N[2017-01-02 15:00:00], until: ~N[2017-01-02 15:15:00], left_open: false, right_open: true)
+
+      assert Interval.new(from: ~N[2017-01-02 15:00:00], until: ~N[2017-01-02 15:15:00], right_open: true, left_open: true) == Interval.overlap(a, b)
+    end
+
+    test "left_open: true, right_open: true" do
+      a = Interval.new(from: ~N[2017-01-02 15:00:00], until: ~N[2017-01-02 15:15:00], right_open: true)
+      b = Interval.new(from: ~N[2017-01-02 15:10:00], until: ~N[2017-01-02 15:30:00], left_open: true)
+
+      assert Interval.new(from: ~N[2017-01-02 15:10:00], until: ~N[2017-01-02 15:15:00], right_open: true, left_open: true) == Interval.overlap(a, b)
+    end
+
+    test "left_open: true, right_open: false" do
+      a = Interval.new(from: ~N[2017-01-02 15:00:00], until: ~N[2017-01-02 15:15:00], right_open: false)
+      b = Interval.new(from: ~N[2017-01-02 15:10:00], until: ~N[2017-01-02 15:30:00], left_open: true)
+
+      assert Interval.new(from: ~N[2017-01-02 15:10:00], until: ~N[2017-01-02 15:15:00], right_open: false, left_open: true) == Interval.overlap(a, b)
+    end
+
+    test "left_open: false, right_open: false" do
+      a = Interval.new(from: ~N[2017-01-02 15:00:00], until: ~N[2017-01-02 15:15:00], right_open: false)
+      b = Interval.new(from: ~N[2017-01-02 15:10:00], until: ~N[2017-01-02 15:30:00], left_open: false)
+
+      assert Interval.new(from: ~N[2017-01-02 15:10:00], until: ~N[2017-01-02 15:15:00], right_open: false, left_open: false) == Interval.overlap(a, b)
+    end
+  end
+
   describe "contains?/2" do
     test "non-overlapping" do
       earlier = Interval.new(from: ~D[2018-01-01], until: ~D[2018-01-04])