diff --git a/core/src/main/scala/cats/Traverse.scala b/core/src/main/scala/cats/Traverse.scala
index 0e05fc45a5c..1eb96ac18f0 100644
--- a/core/src/main/scala/cats/Traverse.scala
+++ b/core/src/main/scala/cats/Traverse.scala
@@ -149,6 +149,22 @@ import scala.annotation.implicitNotFound
 
   override def unorderedSequence[G[_]: CommutativeApplicative, A](fga: F[G[A]]): G[F[A]] =
     sequence(fga)
+
+  /**
+   * a combination of map and scanLeft
+   * it applies a function to each element of a structure,
+   * passing an accumulating parameter from left to right,
+   * and returning a final value of this accumulator together with the new structure.
+   */
+  def mapAccumL[A, B, C](fa: F[A], start: B)(step: (B, A) => (B, C)): (B, F[C]) =
+    traverse(fa)(a => State((b: B) => step(b, a))).run(start).value
+
+  /**
+   * like [[mapAccumL]] but also combines monadic effects of `G`
+   * stack-safety relies on a stack safety of G
+   */
+  def mapAccumF[G[_]: Monad, A, B, C](fa: F[A], start: B)(step: (B, A) => G[(B, C)]): G[(B, F[C])] =
+    traverse(fa)(a => StateT((b: B) => step(b, a))).run(start)
 }
 
 object Traverse {
@@ -166,48 +182,38 @@ object Traverse {
   object ops {
     implicit def toAllTraverseOps[F[_], A](target: F[A])(implicit tc: Traverse[F]): AllOps[F, A] {
       type TypeClassType = Traverse[F]
-    } =
-      new AllOps[F, A] {
-        type TypeClassType = Traverse[F]
-        val self: F[A] = target
-        val typeClassInstance: TypeClassType = tc
-      }
+    } = new AllOps[F, A] {
+      type TypeClassType = Traverse[F]
+      val self: F[A] = target
+      val typeClassInstance: TypeClassType = tc
+    }
   }
   trait Ops[F[_], A] extends Serializable {
     type TypeClassType <: Traverse[F]
     def self: F[A]
     val typeClassInstance: TypeClassType
-    def traverse[G[_], B](f: A => G[B])(implicit ev$1: Applicative[G]): G[F[B]] =
-      typeClassInstance.traverse[G, A, B](self)(f)
-    def traverseTap[G[_], B](f: A => G[B])(implicit ev$1: Applicative[G]): G[F[A]] =
-      typeClassInstance.traverseTap[G, A, B](self)(f)
-    def flatTraverse[G[_], B](f: A => G[F[B]])(implicit G: Applicative[G], F: FlatMap[F]): G[F[B]] =
-      typeClassInstance.flatTraverse[G, A, B](self)(f)(G, F)
-    def sequence[G[_], B](implicit ev$1: A <:< G[B], ev$2: Applicative[G]): G[F[B]] =
-      typeClassInstance.sequence[G, B](self.asInstanceOf[F[G[B]]])
-    def flatSequence[G[_], B](implicit ev$1: A <:< G[F[B]], G: Applicative[G], F: FlatMap[F]): G[F[B]] =
-      typeClassInstance.flatSequence[G, B](self.asInstanceOf[F[G[F[B]]]])(G, F)
+    def traverse[G[_], B](f: A => G[B])(implicit ev$1: Applicative[G]): G[F[B]] = typeClassInstance.traverse[G, A, B](self)(f)
+    def traverseTap[G[_], B](f: A => G[B])(implicit ev$1: Applicative[G]): G[F[A]] = typeClassInstance.traverseTap[G, A, B](self)(f)
+    def flatTraverse[G[_], B](f: A => G[F[B]])(implicit G: Applicative[G], F: FlatMap[F]): G[F[B]] = typeClassInstance.flatTraverse[G, A, B](self)(f)(G, F)
+    def sequence[G[_], B](implicit ev$1: A <:< G[B], ev$2: Applicative[G]): G[F[B]] = typeClassInstance.sequence[G, B](self.asInstanceOf[F[G[B]]])
+    def flatSequence[G[_], B](implicit ev$1: A <:< G[F[B]], G: Applicative[G], F: FlatMap[F]): G[F[B]] = typeClassInstance.flatSequence[G, B](self.asInstanceOf[F[G[F[B]]]])(G, F)
     def mapWithIndex[B](f: (A, Int) => B): F[B] = typeClassInstance.mapWithIndex[A, B](self)(f)
-    def traverseWithIndexM[G[_], B](f: (A, Int) => G[B])(implicit G: Monad[G]): G[F[B]] =
-      typeClassInstance.traverseWithIndexM[G, A, B](self)(f)(G)
+    def traverseWithIndexM[G[_], B](f: (A, Int) => G[B])(implicit G: Monad[G]): G[F[B]] = typeClassInstance.traverseWithIndexM[G, A, B](self)(f)(G)
     def zipWithIndex: F[(A, Int)] = typeClassInstance.zipWithIndex[A](self)
+    def mapAccumL[B, C](start: B)(step: (B, A) => (B, C)): (B, F[C]) = typeClassInstance.mapAccumL[A, B, C](self, start)(step)
+    def mapAccumF[G[_], B, C](start: B)(step: (B, A) => G[(B, C)])(implicit ev$1: Monad[G]): G[(B, F[C])] = typeClassInstance.mapAccumF[G, A, B, C](self, start)(step)
   }
-  trait AllOps[F[_], A]
-      extends Ops[F, A]
-      with Functor.AllOps[F, A]
-      with Foldable.AllOps[F, A]
-      with UnorderedTraverse.AllOps[F, A] {
+  trait AllOps[F[_], A] extends Ops[F, A] with Functor.AllOps[F, A] with Foldable.AllOps[F, A] with UnorderedTraverse.AllOps[F, A] {
     type TypeClassType <: Traverse[F]
   }
   trait ToTraverseOps extends Serializable {
     implicit def toTraverseOps[F[_], A](target: F[A])(implicit tc: Traverse[F]): Ops[F, A] {
       type TypeClassType = Traverse[F]
-    } =
-      new Ops[F, A] {
-        type TypeClassType = Traverse[F]
-        val self: F[A] = target
-        val typeClassInstance: TypeClassType = tc
-      }
+    } = new Ops[F, A] {
+      type TypeClassType = Traverse[F]
+      val self: F[A] = target
+      val typeClassInstance: TypeClassType = tc
+    }
   }
   @deprecated("Use cats.syntax object imports", "2.2.0")
   object nonInheritedOps extends ToTraverseOps
@@ -216,4 +222,10 @@ object Traverse {
   /* END OF SIMULACRUM-MANAGED CODE                                           */
   /* ======================================================================== */
 
+
+
+
+
+
+
 }
diff --git a/tests/src/test/scala/cats/tests/TraverseSuite.scala b/tests/src/test/scala/cats/tests/TraverseSuite.scala
index 1138952be14..9e617ef3ca5 100644
--- a/tests/src/test/scala/cats/tests/TraverseSuite.scala
+++ b/tests/src/test/scala/cats/tests/TraverseSuite.scala
@@ -32,6 +32,18 @@ abstract class TraverseSuite[F[_]: Traverse](name: String)(implicit ArbFInt: Arb
     }
   }
 
+  test(s"Traverse[$name].mapAccumL") {
+    forAll { (fa: F[Int], start: Long, fn: (Long, Int) => (Long, Int)) =>
+      val (act, fb) = fa.mapAccumL(start)(fn)
+      val (exp, xs) = fa.toList.foldLeft((start, List.empty[Int])) { case ((prev, acc), a) =>
+        val (next, b) = fn(prev, a)
+        (next, b :: acc)
+      }
+      assert(act === exp)
+      assert(fb.toList === xs.reverse)
+    }
+  }
+
 }
 
 object TraverseSuite {