diff --git a/core/src/main/scala/cats/data/NonEmptyList.scala b/core/src/main/scala/cats/data/NonEmptyList.scala
index 4dfc37dc61..946729b011 100644
--- a/core/src/main/scala/cats/data/NonEmptyList.scala
+++ b/core/src/main/scala/cats/data/NonEmptyList.scala
@@ -66,6 +66,8 @@ final case class NonEmptyList[+A](head: A, tail: List[A]) {
    */
   def size: Int = 1 + tail.size
 
+  def length: Int = size
+
   /**
    *  Applies f to all the elements of the structure
    */
@@ -73,12 +75,28 @@ final case class NonEmptyList[+A](head: A, tail: List[A]) {
     NonEmptyList(f(head), tail.map(f))
 
   def ++[AA >: A](l: List[AA]): NonEmptyList[AA] =
-    NonEmptyList(head, tail ++ l)
+    concat(l)
+
+  def concat[AA >: A](other: List[AA]): NonEmptyList[AA] =
+    NonEmptyList(head, tail ::: other)
+
+  @deprecated("Use concatNel", since = "1.0.0-RC1")
+  def concat[AA >: A](other: NonEmptyList[AA]): NonEmptyList[AA] =
+    concatNel(other)
+
+  /**
+   * Append another NonEmptyList
+   */
+  def concatNel[AA >: A](other: NonEmptyList[AA]): NonEmptyList[AA] =
+    NonEmptyList(head, tail ::: other.toList)
 
   def flatMap[B](f: A => NonEmptyList[B]): NonEmptyList[B] =
     f(head) ++ tail.flatMap(f andThen (_.toList))
 
   def ::[AA >: A](a: AA): NonEmptyList[AA] =
+    prepend(a)
+
+  def prepend[AA >: A](a: AA): NonEmptyList[AA] =
     NonEmptyList(a, head :: tail)
 
   /**
@@ -137,12 +155,6 @@ final case class NonEmptyList[+A](head: A, tail: List[A]) {
     }
   }
 
-  /**
-   * Append another NonEmptyList
-   */
-  def concat[AA >: A](other: NonEmptyList[AA]): NonEmptyList[AA] =
-    NonEmptyList(head, tail ::: other.toList)
-
   /**
    * Find the first element matching the predicate, if one exists
    */
@@ -405,7 +417,7 @@ private[data] sealed abstract class NonEmptyListInstances extends NonEmptyListIn
       with Monad[NonEmptyList] with NonEmptyTraverse[NonEmptyList] {
 
       def combineK[A](a: NonEmptyList[A], b: NonEmptyList[A]): NonEmptyList[A] =
-        a concat b
+        a concatNel b
 
       override def split[A](fa: NonEmptyList[A]): (A, List[A]) = (fa.head, fa.tail)
 
diff --git a/core/src/main/scala/cats/data/NonEmptyVector.scala b/core/src/main/scala/cats/data/NonEmptyVector.scala
index 9fdeebd230..0750618411 100644
--- a/core/src/main/scala/cats/data/NonEmptyVector.scala
+++ b/core/src/main/scala/cats/data/NonEmptyVector.scala
@@ -36,6 +36,10 @@ final class NonEmptyVector[+A] private (val toVector: Vector[A]) extends AnyVal
 
   def tail: Vector[A] = toVector.tail
 
+  def last: A = toVector.last
+
+  def init: Vector[A] = toVector.init
+
   /**
     * Remove elements not matching the predicate
     *
@@ -60,6 +64,8 @@ final class NonEmptyVector[+A] private (val toVector: Vector[A]) extends AnyVal
     */
   def filterNot(f: A => Boolean): Vector[A] = toVector.filterNot(f)
 
+  def collect[B](pf: PartialFunction[A, B]): Vector[B] = toVector.collect(pf)
+
   /**
    * Alias for [[concat]]
    */
@@ -198,6 +204,18 @@ final class NonEmptyVector[+A] private (val toVector: Vector[A]) extends AnyVal
     */
   def zipWith[B, C](b: NonEmptyVector[B])(f: (A, B) => C): NonEmptyVector[C] =
     NonEmptyVector.fromVectorUnsafe((toVector, b.toVector).zipped.map(f))
+
+  def reverse: NonEmptyVector[A] =
+    new NonEmptyVector(toVector.reverse)
+
+  def zipWithIndex: NonEmptyVector[(A, Int)] =
+    new NonEmptyVector(toVector.zipWithIndex)
+
+  def sortBy[B](f: A => B)(implicit B: Order[B]): NonEmptyVector[A] =
+    new NonEmptyVector(toVector.sortBy(f)(B.toOrdering))
+
+  def sorted[AA >: A](implicit AA: Order[AA]): NonEmptyVector[AA] =
+    new NonEmptyVector(toVector.sorted(AA.toOrdering))
 }
 
 private[data] sealed abstract class NonEmptyVectorInstances {
@@ -251,6 +269,9 @@ private[data] sealed abstract class NonEmptyVectorInstances {
       override def traverse[G[_], A, B](fa: NonEmptyVector[A])(f: (A) => G[B])(implicit G: Applicative[G]): G[NonEmptyVector[B]] =
         G.map2Eval(f(fa.head), Always(Traverse[Vector].traverse(fa.tail)(f)))(NonEmptyVector(_, _)).value
 
+      override def zipWithIndex[A](fa: NonEmptyVector[A]): NonEmptyVector[(A, Int)] =
+        fa.zipWithIndex
+
       override def foldLeft[A, B](fa: NonEmptyVector[A], b: B)(f: (B, A) => B): B =
         fa.foldLeft(b)(f)
 
diff --git a/tests/src/test/scala/cats/tests/NonEmptyVectorTests.scala b/tests/src/test/scala/cats/tests/NonEmptyVectorTests.scala
index 93b3284d34..7bd91690d0 100644
--- a/tests/src/test/scala/cats/tests/NonEmptyVectorTests.scala
+++ b/tests/src/test/scala/cats/tests/NonEmptyVectorTests.scala
@@ -317,12 +317,19 @@ class NonEmptyVectorTests extends CatsSuite {
     }
   }
 
-
   test("NonEmptyVector#zipWith is consistent with Vector#zip and then Vector#map") {
     forAll { (a: NonEmptyVector[Int], b: NonEmptyVector[Int], f: (Int, Int) => Int) =>
       a.zipWith(b)(f).toVector should ===(a.toVector.zip(b.toVector).map { case (x, y) => f(x, y) })
     }
   }
+
+  test("NonEmptyVector#zipWith is consistent with #zipWithIndex") {
+    forAll { nev: NonEmptyVector[Int] =>
+      val zw = nev.zipWith(NonEmptyVector.fromVectorUnsafe((0 until nev.length).toVector))(Tuple2.apply)
+      nev.zipWithIndex should === (zw)
+    }
+  }
+
   test("NonEmptyVector#nonEmptyPartition remains sorted") {
     forAll { (nev: NonEmptyVector[Int], f: Int => Either[String, String]) =>
 
@@ -333,6 +340,55 @@ class NonEmptyVectorTests extends CatsSuite {
       ior.right.map(xs => xs.sorted should === (xs))
     }
   }
+
+  test("NonEmptyVector#last is consistent with Vector#last") {
+    forAll { nonEmptyVector: NonEmptyVector[Int] =>
+      nonEmptyVector.last should === (nonEmptyVector.toVector.last)
+    }
+  }
+
+  test("NonEmptyVector#init is consistent with Vector#init") {
+    forAll { nonEmptyVector: NonEmptyVector[Int] =>
+      nonEmptyVector.init should === (nonEmptyVector.toVector.init)
+    }
+  }
+
+  test("NonEmptyVector#collect is consistent with Vector#collect") {
+    val pf: PartialFunction[Int, Double] = {
+      case i if (i % 2 == 0) => i.toDouble
+    }
+    forAll { nonEmptyVector: NonEmptyVector[Int] =>
+      nonEmptyVector.collect(pf) should === (nonEmptyVector.toVector.collect(pf))
+    }
+  }
+
+  test("NonEmptyVector#length and size is consistent with Vector#length") {
+    forAll { nonEmptyVector: NonEmptyVector[Int] =>
+      nonEmptyVector.length should === (nonEmptyVector.toVector.length)
+      nonEmptyVector.size should === (nonEmptyVector.toVector.length.toLong)
+    }
+  }
+
+  test("NonEmptyVector#reverse is consistent with Vector#reverse") {
+    forAll { nonEmptyVector: NonEmptyVector[Int] =>
+      nonEmptyVector.reverse should === (NonEmptyVector.fromVectorUnsafe(nonEmptyVector.toVector.reverse))
+    }
+  }
+
+  test("NonEmptyVector#zipWithIndex is consistent with Vector#zipWithIndex") {
+    forAll { nonEmptyVector: NonEmptyVector[Int] =>
+      val expected = NonEmptyVector.fromVectorUnsafe(nonEmptyVector.toVector.zipWithIndex)
+      nonEmptyVector.zipWithIndex should === (expected)
+      Traverse[NonEmptyVector].zipWithIndex(nonEmptyVector) should === (expected)
+    }
+  }
+
+  test("NonEmptyVector#sorted and sortBy is consistent with Vector#sorted and sortBy") {
+    forAll { nonEmptyVector: NonEmptyVector[Int] =>
+      nonEmptyVector.sorted should === (NonEmptyVector.fromVectorUnsafe(nonEmptyVector.toVector.sorted))
+      nonEmptyVector.sortBy(i => -i) should === (NonEmptyVector.fromVectorUnsafe(nonEmptyVector.toVector.sortBy(i => -i)))
+    }
+  }
 }
 
 class ReducibleNonEmptyVectorCheck extends ReducibleCheck[NonEmptyVector]("NonEmptyVector") {
diff --git a/tests/src/test/scala/cats/tests/NonEmptyListTests.scala b/tests/src/test/scala/cats/tests/nonEmptyListTests.scala
similarity index 92%
rename from tests/src/test/scala/cats/tests/NonEmptyListTests.scala
rename to tests/src/test/scala/cats/tests/nonEmptyListTests.scala
index 2e1497dcc0..225f7a5f0e 100644
--- a/tests/src/test/scala/cats/tests/NonEmptyListTests.scala
+++ b/tests/src/test/scala/cats/tests/nonEmptyListTests.scala
@@ -224,6 +224,7 @@ class NonEmptyListTests extends CatsSuite {
   test(":: consistent with List") {
     forAll { (nel: NonEmptyList[Int], i: Int) =>
       (i :: nel).toList should === (i :: nel.toList)
+      nel.prepend(i).toList should === (i :: nel.toList)
     }
   }
 
@@ -257,9 +258,10 @@ class NonEmptyListTests extends CatsSuite {
     }
   }
 
-  test("NonEmptyList#size is consistent with List#size") {
+  test("NonEmptyList#size and length is consistent with List#size") {
     forAll { nel: NonEmptyList[Int] =>
       nel.size should === (nel.toList.size)
+      nel.length should === (nel.toList.size)
     }
   }
 
@@ -282,7 +284,15 @@ class NonEmptyListTests extends CatsSuite {
     }
   }
 
-  test("NonEmptyList#fromFoldable is consistent with NonEmptyList#fromList") {
+  test("NonEmptyList#concat/concatNel is consistent with List#:::") {
+    forAll { (nel: NonEmptyList[Int], l: List[Int], n: Int) =>
+      (nel ++ l).toList should === (nel.toList ::: l)
+      nel.concat(l).toList should === (nel.toList ::: l)
+      nel.concatNel(NonEmptyList(n, l)).toList should === (nel.toList ::: (n :: l))
+    }
+  }
+
+  test("NonEmptyList#fromFoldabale is consistent with NonEmptyList#fromList") {
     forAll { (xs: List[Int]) =>
       NonEmptyList.fromList(xs) should === (NonEmptyList.fromFoldable(xs))
     }
@@ -312,6 +322,16 @@ class NonEmptyListTests extends CatsSuite {
   }
 }
 
+@deprecated("to be able to test deprecated methods", since = "1.0.0-RC1")
+class DeprecatedNonEmptyListTests extends CatsSuite {
+
+  test("Deprecated NonEmptyList#concat is consistent with List#:::") {
+    forAll { (nel: NonEmptyList[Int], l: List[Int], n: Int) =>
+      nel.concat(NonEmptyList(n, l)).toList should === (nel.toList ::: (n :: l))
+    }
+  }
+}
+
 class ReducibleNonEmptyListCheck extends ReducibleCheck[NonEmptyList]("NonEmptyList") {
   def iterator[T](nel: NonEmptyList[T]): Iterator[T] = nel.toList.iterator