diff --git a/core/src/main/scala/cats/data/Binested.scala b/core/src/main/scala/cats/data/Binested.scala
new file mode 100644
index 00000000000..5ce3a8fc228
--- /dev/null
+++ b/core/src/main/scala/cats/data/Binested.scala
@@ -0,0 +1,93 @@
+package cats
+package data
+
+import cats.arrow._
+
+/** Compose a two-slot type constructor `F[_, _]` with two single-slot type constructors
+ *  `G[_]` and `H[_]`, resulting in a two-slot type constructor with respect to the inner types.
+ *  For example, `List` and `Option` both have `Functor` instances, and `Either` has a
+ *  `Bifunctor` instance. Therefore, `Binested[Either, List, Option, ?, ?]` has a `Bifunctor`
+ *  instance as well:
+ *
+ * {{{
+ * scala> import cats.Bifunctor
+ * scala> import cats.data.Binested
+ * scala> import cats.implicits._
+ * scala> val eitherListOption: Either[List[Int], Option[String]] = Right(Some("cats"))
+ * scala> val f: Int => String = _.toString
+ * scala> val g: String => String = _ + "-bifunctor"
+ * scala> val binested = Binested(eitherListOption)
+ * scala> val bimapped = Bifunctor[Binested[Either, List, Option, ?, ?]].bimap(binested)(f, g).value
+ * res0: Either[List[String], Option[String]] = Right(Some("cats-bifunctor"))
+ * }}}
+ */
+final case class Binested[F[_, _], G[_], H[_], A, B](value: F[G[A], H[B]])
+
+object Binested extends BinestedInstances
+
+trait BinestedInstances extends BinestedInstances0 {
+  implicit def catsDataEqForBinested[F[_, _], G[_], H[_], A, B](
+    implicit F: Eq[F[G[A], H[B]]]): Eq[Binested[F, G, H, A, B]] =
+    Eq.by(_.value)
+
+  implicit def catsDataBifunctorForBinested[F[_, _], G[_], H[_]](
+    implicit F: Bifunctor[F], G: Functor[G], H: Functor[H]): Bifunctor[Binested[F, G, H, ?, ?]] =
+    new Bifunctor[Binested[F, G, H, ?, ?]] {
+      def bimap[A, B, C, D](fab: Binested[F, G, H, A, B])(f: A => C, g: B => D): Binested[F, G, H, C, D] =
+        Binested(F.bimap(fab.value)(G.map(_)(f), H.map(_)(g)))
+    }
+
+  implicit def catsDataProfunctorForBinested[F[_, _], G[_], H[_]](
+    implicit F: Profunctor[F], G: Functor[G], H: Functor[H]): Profunctor[Binested[F, G, H, ?, ?]] =
+    new Profunctor[Binested[F, G, H, ?, ?]] {
+      def dimap[A, B, C, D](fab: Binested[F, G, H, A, B])(f: C => A)(g: B => D): Binested[F, G, H, C, D] =
+        Binested(F.dimap(fab.value)(G.map(_: G[C])(f))(H.map(_)(g)))
+    }
+
+  implicit def catsDataBifoldableForBinested[F[_, _], G[_], H[_]](
+    implicit F0: Bifoldable[F], G0: Foldable[G], H0: Foldable[H]): Bifoldable[Binested[F, G, H, ?, ?]] =
+    new BinestedBifoldable[F, G, H] {
+      override implicit def F: Bifoldable[F] = F0
+      override implicit def G: Foldable[G] = G0
+      override implicit def H: Foldable[H] = H0
+    }
+}
+
+trait BinestedInstances0 {
+  implicit def catsDataBitraverseForBinested[F[_, _], G[_], H[_]](
+    implicit F0: Bitraverse[F], H0: Traverse[H], G0: Traverse[G]): Bitraverse[Binested[F, G, H, ?, ?]] =
+    new BinestedBitraverse[F, G, H] {
+      override implicit def F: Bitraverse[F] = F0
+      override implicit def G: Traverse[G] = G0
+      override implicit def H: Traverse[H] = H0
+    }
+}
+
+sealed abstract class BinestedBifoldable[F[_, _], G[_], H[_]] extends Bifoldable[Binested[F, G, H, ?, ?]] {
+  implicit def F: Bifoldable[F]
+  implicit def G: Foldable[G]
+  implicit def H: Foldable[H]
+
+  def bifoldLeft[A, B, C](fab: Binested[F, G, H, A, B], c: C)(f: (C, A) => C, g: (C, B) => C): C =
+    F.bifoldLeft(fab.value, c)(
+      (c, ga) => G.foldLeft(ga, c)(f),
+      (c, hb) => H.foldLeft(hb, c)(g)
+    )
+
+
+  def bifoldRight[A, B, C](fab: Binested[F, G, H, A, B], c: Eval[C])(f: (A, Eval[C]) => Eval[C], g: (B, Eval[C]) => Eval[C]): Eval[C] =
+    F.bifoldRight(fab.value, c)(
+      (ga, ec) => G.foldRight(ga, ec)(f),
+      (hb, ec) => H.foldRight(hb, ec)(g)
+    )
+}
+
+sealed abstract class BinestedBitraverse[F[_, _], G[_], H[_]] extends BinestedBifoldable[F, G, H] with Bitraverse[Binested[F, G, H, ?, ?]] {
+  override implicit def F: Bitraverse[F]
+  override implicit def G: Traverse[G]
+  override implicit def H: Traverse[H]
+
+  def bitraverse[I[_], A, B, C, D](fab: Binested[F, G, H, A, B])(f: A => I[C], g: B => I[D])(implicit I: Applicative[I]): I[Binested[F, G, H, C, D]] = {
+    I.map(F.bitraverse(fab.value)(G.traverse(_)(f), H.traverse(_)(g)))(Binested(_))
+  }
+}
diff --git a/core/src/main/scala/cats/syntax/all.scala b/core/src/main/scala/cats/syntax/all.scala
index dec09ed8e05..8e58a8e74f3 100644
--- a/core/src/main/scala/cats/syntax/all.scala
+++ b/core/src/main/scala/cats/syntax/all.scala
@@ -58,5 +58,6 @@ trait AllSyntaxBinCompat0
     extends UnorderedTraverseSyntax
     with ApplicativeErrorExtension
     with TrySyntax
+    with BinestedSyntax
 
 trait AllSyntaxBinCompat1 extends FlatMapOptionSyntax
diff --git a/core/src/main/scala/cats/syntax/binested.scala b/core/src/main/scala/cats/syntax/binested.scala
new file mode 100644
index 00000000000..32a8016fbc8
--- /dev/null
+++ b/core/src/main/scala/cats/syntax/binested.scala
@@ -0,0 +1,13 @@
+package cats
+package syntax
+
+import cats.data.Binested
+
+trait BinestedSyntax {
+  implicit final def catsSyntaxBinestedId[F[_, _], G[_], H[_], A, B](value: F[G[A], H[B]]): BinestedIdOps[F, G, H, A, B] =
+    new BinestedIdOps(value)
+}
+
+final class BinestedIdOps[F[_, _], G[_], H[_], A, B](val value: F[G[A], H[B]]) extends AnyVal {
+  def binested: Binested[F, G, H, A, B] = Binested(value)
+}
diff --git a/core/src/main/scala/cats/syntax/package.scala b/core/src/main/scala/cats/syntax/package.scala
index b928818bc9c..b49683707ce 100644
--- a/core/src/main/scala/cats/syntax/package.scala
+++ b/core/src/main/scala/cats/syntax/package.scala
@@ -10,6 +10,7 @@ package object syntax {
   object arrowChoice extends ArrowChoiceSyntax
   object bifunctor extends BifunctorSyntax
   object bifoldable extends BifoldableSyntax
+  object binested extends BinestedSyntax
   object bitraverse extends BitraverseSyntax
   @deprecated("use cats.syntax.semigroupal instead", "1.0.0-RC1")
   object cartesian extends SemigroupalSyntax
diff --git a/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala b/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala
index fce94163b4d..63f7df25718 100644
--- a/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala
+++ b/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala
@@ -228,6 +228,9 @@ object arbitrary extends ArbitraryInstances0 {
   implicit def catsLawsArbitraryForNested[F[_], G[_], A](implicit FG: Arbitrary[F[G[A]]]): Arbitrary[Nested[F, G, A]] =
     Arbitrary(FG.arbitrary.map(Nested(_)))
 
+  implicit def catsLawsArbitraryForBinested[F[_, _], G[_], H[_], A, B](implicit F: Arbitrary[F[G[A], H[B]]]): Arbitrary[Binested[F, G, H, A, B]] =
+    Arbitrary(F.arbitrary.map(Binested(_)))
+
   implicit def catsLawArbitraryForState[S: Arbitrary: Cogen, A: Arbitrary]: Arbitrary[State[S, A]] =
     catsLawArbitraryForIndexedStateT[Eval, S, S, A]
 
diff --git a/tests/src/test/scala/cats/tests/BinestedSuite.scala b/tests/src/test/scala/cats/tests/BinestedSuite.scala
new file mode 100644
index 00000000000..29c4fae1e4d
--- /dev/null
+++ b/tests/src/test/scala/cats/tests/BinestedSuite.scala
@@ -0,0 +1,45 @@
+package cats
+package tests
+
+import cats.arrow.Profunctor
+import cats.data.Binested
+
+import cats.laws.discipline._
+import cats.laws.discipline.arbitrary._
+import cats.laws.discipline.eq._
+
+class BinestedSuite extends CatsSuite {
+  // we have a lot of generated lists of lists in these tests. We have to tell
+  // Scalacheck to calm down a bit so we don't hit memory and test duration
+  // issues.
+  implicit override val generatorDrivenConfig: PropertyCheckConfiguration =
+    PropertyCheckConfiguration(minSuccessful = 20, sizeRange = 5)
+
+  {
+    // Bifunctor + Functor + Functor = Bifunctor
+    implicit val instance = ListWrapper.functor
+    checkAll("Binested[Either, ListWrapper, Option, ?, ?]", BifunctorTests[Binested[Either, ListWrapper, Option, ?, ?]].bifunctor[Int, Int, Int, String, String, String])
+    checkAll("Bifunctor[Binested[Either, ListWrapper, Option, ?, ?]]", SerializableTests.serializable(Bifunctor[Binested[Either, ListWrapper, Option, ?, ?]]))
+  }
+
+  {
+    // Profunctor + Functor + Functor = Profunctor
+    implicit val instance = ListWrapper.functor
+    checkAll("Binested[Function1, ListWrapper, Option, ?, ?]", ProfunctorTests[Binested[Function1, ListWrapper, Option, ?, ?]].profunctor[Int, Int, Int, String, String, String])
+    checkAll("Profunctor[Binested[Function1, ListWrapper, Option, ?, ?]]", SerializableTests.serializable(Profunctor[Binested[Function1, ListWrapper, Option, ?, ?]]))
+  }
+
+  {
+    // Bifoldable + foldable + foldable = Bifoldable
+    implicit val instance = ListWrapper.foldable
+    checkAll("Binested[Either, ListWrapper, ListWrapper, ?, ?]", BifoldableTests[Binested[Either, ListWrapper, ListWrapper, ?, ?]].bifoldable[Int, Int, Int])
+    checkAll("Bifoldable[Binested[Either, ListWrapper, ListWrapper, ?, ?]]", SerializableTests.serializable(Bifoldable[Binested[Either, ListWrapper, ListWrapper, ?, ?]]))
+  }
+
+  {
+    // Bitraverse + traverse + traverse = Bitraverse
+    implicit val instance = ListWrapper.traverse
+    checkAll("Binested[Either, ListWrapper, ListWrapper, ?, ?]", BitraverseTests[Binested[Either, ListWrapper, ListWrapper, ?, ?]].bitraverse[Option, Int, Int, Int, String, String, String])
+    checkAll("Bitraverse[Binested[Either, ListWrapper, ListWrapper, ?, ?]]", SerializableTests.serializable(Bitraverse[Binested[Either, ListWrapper, ListWrapper, ?, ?]]))
+  }
+}
diff --git a/tests/src/test/scala/cats/tests/SyntaxSuite.scala b/tests/src/test/scala/cats/tests/SyntaxSuite.scala
index 6bcd3b987b4..2b6a46f25cf 100644
--- a/tests/src/test/scala/cats/tests/SyntaxSuite.scala
+++ b/tests/src/test/scala/cats/tests/SyntaxSuite.scala
@@ -2,8 +2,9 @@ package cats
 package tests
 
 import cats.arrow.Compose
+import cats.data.Binested
 import cats.instances.AllInstances
-import cats.syntax.AllSyntax
+import cats.syntax.{ AllSyntax, AllSyntaxBinCompat }
 
 
 /**
@@ -24,7 +25,7 @@ import cats.syntax.AllSyntax
  *
  * None of these tests should ever run, or do any runtime checks.
  */
-object SyntaxSuite extends AllInstances with AllSyntax {
+object SyntaxSuite extends AllSyntaxBinCompat with AllInstances with AllSyntax {
 
   // pretend we have a value of type A
   def mock[A]: A = ???
@@ -338,5 +339,10 @@ object SyntaxSuite extends AllInstances with AllSyntax {
     val gea4 = ga.recoverWith(pfegea)
   }
 
+  def testBinested[F[_, _], G[_], H[_], A, B]: Unit = {
+    val fgahb = mock[F[G[A], H[B]]]
+
+    val binested: Binested[F, G, H, A, B] = fgahb.binested
+  }
 }