diff --git a/core/src/main/scala/cats/implicits.scala b/core/src/main/scala/cats/implicits.scala
index 350fc9fb9b..d89f1f1d46 100644
--- a/core/src/main/scala/cats/implicits.scala
+++ b/core/src/main/scala/cats/implicits.scala
@@ -7,3 +7,4 @@ object implicits
     with syntax.AllSyntaxBinCompat2
     with instances.AllInstances
     with instances.AllInstancesBinCompat0
+    with instances.AllInstancesBinCompat1
diff --git a/core/src/main/scala/cats/instances/all.scala b/core/src/main/scala/cats/instances/all.scala
index d8c3361fa2..5d82c6d715 100644
--- a/core/src/main/scala/cats/instances/all.scala
+++ b/core/src/main/scala/cats/instances/all.scala
@@ -36,3 +36,6 @@ trait AllInstances
 trait AllInstancesBinCompat0
     extends FunctionInstancesBinCompat0
     with    Tuple2InstancesBinCompat0
+
+trait AllInstancesBinCompat1
+    extends MapInstancesBinCompat0
diff --git a/core/src/main/scala/cats/instances/map.scala b/core/src/main/scala/cats/instances/map.scala
index 573ce85556..dd044faf36 100644
--- a/core/src/main/scala/cats/instances/map.scala
+++ b/core/src/main/scala/cats/instances/map.scala
@@ -4,6 +4,7 @@ package instances
 import cats.kernel.CommutativeMonoid
 
 import scala.annotation.tailrec
+import cats.arrow.Compose
 
 trait MapInstances extends cats.kernel.instances.MapInstances {
 
@@ -79,4 +80,34 @@ trait MapInstances extends cats.kernel.instances.MapInstances {
 
     }
   // scalastyle:on method.length
+
+}
+
+trait MapInstancesBinCompat0 {
+
+  implicit val catsStdComposeForMap: Compose[Map] = new Compose[Map] {
+
+    /**
+      * Compose two maps `g` and `f` by using the values in `f` as keys for `g`.
+      * {{{
+      * scala> import cats.arrow.Compose
+      * scala> import cats.implicits._
+      * scala> val first = Map(1 -> "a", 2 -> "b", 3 -> "c", 4 -> "a")
+      * scala> val second = Map("a" -> true, "b" -> false, "d" -> true)
+      * scala> Compose[Map].compose(second, first)
+      * res0: Map[Int, Boolean] = Map(1 -> true, 2 -> false, 4 -> true)
+      * }}}
+      */
+    def compose[A, B, C](f: Map[B, C], g: Map[A, B]): Map[A, C] = {
+      g.foldLeft(Map.empty[A, C]) {
+        case (acc, (key, value)) =>
+          f.get(value) match {
+            case Some(other) => acc + (key -> other)
+            case _ => acc
+          }
+      }
+    }
+
+  }
+
 }
diff --git a/core/src/main/scala/cats/instances/package.scala b/core/src/main/scala/cats/instances/package.scala
index 13f70fc8ee..f398b3ad65 100644
--- a/core/src/main/scala/cats/instances/package.scala
+++ b/core/src/main/scala/cats/instances/package.scala
@@ -1,7 +1,7 @@
 package cats
 
 package object instances {
-  object all             extends AllInstances with AllInstancesBinCompat0
+  object all             extends AllInstances with AllInstancesBinCompat0 with AllInstancesBinCompat1
   object bigInt          extends BigIntInstances
   object bigDecimal      extends BigDecimalInstances
   object bitSet          extends BitSetInstances
@@ -21,7 +21,7 @@ package object instances {
   object invariant       extends InvariantMonoidalInstances
   object list            extends ListInstances
   object long            extends LongInstances
-  object map             extends MapInstances
+  object map             extends MapInstances with MapInstancesBinCompat0
   object option          extends OptionInstances
   object order           extends OrderInstances
   object ordering        extends OrderingInstances
diff --git a/testkit/src/main/scala/cats/tests/CatsSuite.scala b/testkit/src/main/scala/cats/tests/CatsSuite.scala
index 617712c2b6..fac621f4dd 100644
--- a/testkit/src/main/scala/cats/tests/CatsSuite.scala
+++ b/testkit/src/main/scala/cats/tests/CatsSuite.scala
@@ -2,7 +2,7 @@ package cats
 package tests
 
 import catalysts.Platform
-import cats.instances.{AllInstances, AllInstancesBinCompat0}
+import cats.instances.{AllInstances, AllInstancesBinCompat0, AllInstancesBinCompat1}
 import cats.syntax.{AllSyntax, AllSyntaxBinCompat0, AllSyntaxBinCompat1, AllSyntaxBinCompat2, EqOps}
 import org.scalactic.anyvals.{PosInt, PosZDouble, PosZInt}
 import org.scalatest.{FunSuite, FunSuiteLike, Matchers}
@@ -33,7 +33,7 @@ trait CatsSuite extends FunSuite
     with GeneratorDrivenPropertyChecks
     with Discipline
     with TestSettings
-    with AllInstances with AllInstancesBinCompat0
+    with AllInstances with AllInstancesBinCompat0 with AllInstancesBinCompat1
     with AllSyntax with AllSyntaxBinCompat0 with AllSyntaxBinCompat1
     with AllSyntaxBinCompat2
     with StrictCatsEquality { self: FunSuiteLike =>
diff --git a/tests/src/test/scala/cats/tests/MapSuite.scala b/tests/src/test/scala/cats/tests/MapSuite.scala
index 9be630d7b5..53fdb73b75 100644
--- a/tests/src/test/scala/cats/tests/MapSuite.scala
+++ b/tests/src/test/scala/cats/tests/MapSuite.scala
@@ -1,7 +1,8 @@
 package cats
 package tests
 
-import cats.laws.discipline.{FlatMapTests, SemigroupalTests, SerializableTests, UnorderedTraverseTests}
+import cats.arrow.Compose
+import cats.laws.discipline.{FlatMapTests, SemigroupalTests, SerializableTests, UnorderedTraverseTests, ComposeTests}
 
 class MapSuite extends CatsSuite {
   implicit val iso = SemigroupalTests.Isomorphisms.invariant[Map[Int, ?]]
@@ -15,6 +16,9 @@ class MapSuite extends CatsSuite {
   checkAll("Map[Int, Int] with Option", UnorderedTraverseTests[Map[Int, ?]].unorderedTraverse[Int, Int, Int, Option, Option])
   checkAll("UnorderedTraverse[Map[Int, ?]]", SerializableTests.serializable(UnorderedTraverse[Map[Int, ?]]))
 
+  checkAll("Map[Int, Long]", ComposeTests[Map].compose[Int, Long, String, Double])
+  checkAll("Compose[Map]", SerializableTests.serializable(Compose[Map]))
+
 
   test("show isn't empty and is formatted as expected") {
     forAll { (map: Map[Int, String]) =>