diff --git a/tests/shared/src/test/scala-2.13+/cats/tests/ScalaVersionSpecific.scala b/tests/shared/src/test/scala-2.13+/cats/tests/ScalaVersionSpecific.scala
index 1efbd376a0..0aa3bdd8fc 100644
--- a/tests/shared/src/test/scala-2.13+/cats/tests/ScalaVersionSpecific.scala
+++ b/tests/shared/src/test/scala-2.13+/cats/tests/ScalaVersionSpecific.scala
@@ -179,7 +179,7 @@ trait ScalaVersionSpecificRegressionSuite { self: RegressionSuite =>
     // shouldn't have ever evaluated validate(8)
     checkAndResetCount(3)
 
-    assert(LazyList(1, 2, 6, 8).traverse_(validate) === (Either.left("6 is greater than 5")))
+    assert(LazyList(1, 2, 6, 8).traverseVoid(validate) === Either.left("6 is greater than 5"))
     checkAndResetCount(3)
   }
 }
diff --git a/tests/shared/src/test/scala/cats/tests/KleisliSuite.scala b/tests/shared/src/test/scala/cats/tests/KleisliSuite.scala
index 56de674069..c7a8ec034c 100644
--- a/tests/shared/src/test/scala/cats/tests/KleisliSuite.scala
+++ b/tests/shared/src/test/scala/cats/tests/KleisliSuite.scala
@@ -378,16 +378,16 @@ class KleisliSuite extends CatsSuite {
     assertEquals(program.run(A123), List((1, "2", true)))
   }
 
-  test("traverse_ doesn't stack overflow") {
+  test("traverseVoid doesn't stack overflow") {
     // see: https://github.com/typelevel/cats/issues/3947
-    val resL = (1 to 10000).toList.traverse_(_ => Kleisli.liftF[Id, String, Unit](())).run("")
-    val resV = (1 to 10000).toVector.traverse_(_ => Kleisli.liftF[Id, String, Unit](())).run("")
+    val resL = (1 to 10000).toList.traverseVoid(_ => Kleisli.liftF[Id, String, Unit](())).run("")
+    val resV = (1 to 10000).toVector.traverseVoid(_ => Kleisli.liftF[Id, String, Unit](())).run("")
     assert(resL === resV)
   }
 
-  test("traverse_ doesn't stack overflow with List + Eval") {
+  test("traverseVoid doesn't stack overflow with List + Eval") {
     // see: https://github.com/typelevel/cats/issues/3947
-    (1 to 10000).toList.traverse_(_ => Kleisli.liftF[Eval, String, Unit](Eval.Unit)).run("").value
+    (1 to 10000).toList.traverseVoid(_ => Kleisli.liftF[Eval, String, Unit](Eval.Unit)).run("").value
   }
 
   /**
diff --git a/tests/shared/src/test/scala/cats/tests/ParallelSuite.scala b/tests/shared/src/test/scala/cats/tests/ParallelSuite.scala
index 869b2611b5..4dc50a6d20 100644
--- a/tests/shared/src/test/scala/cats/tests/ParallelSuite.scala
+++ b/tests/shared/src/test/scala/cats/tests/ParallelSuite.scala
@@ -78,24 +78,24 @@ class ParallelSuite
     }
   }
 
-  test("ParTraverse_ identity should be equivalent to parSequence_") {
+  test("ParTraverseVoid identity should be equivalent to parSequenceVoid") {
     forAll { (es: SortedSet[Either[String, Int]]) =>
-      assert(Parallel.parTraverse_(es)(identity) === (Parallel.parSequence_[SortedSet, Either[String, *], Int](es)))
+      assert(Parallel.parTraverseVoid(es)(identity) === Parallel.parSequenceVoid[SortedSet, Either[String, *], Int](es))
     }
   }
 
-  test("ParTraverse_ syntax should be equivalent to Parallel.parTraverse_") {
+  test("ParTraverseVoid syntax should be equivalent to Parallel.parTraverseVoid") {
     forAll { (es: SortedSet[Either[String, Int]]) =>
       assert(
-        Parallel.parTraverse_[SortedSet, Either[String, *], Either[String, Int], Int](es)(identity) === (es
-          .parTraverse_(identity))
+        Parallel.parTraverseVoid[SortedSet, Either[String, *], Either[String, Int], Int](es)(identity) ===
+          es.parTraverseVoid(identity)
       )
     }
   }
 
-  test("ParSequence_ syntax should be equivalent to Parallel.parSequence_") {
+  test("ParSequenceVoid syntax should be equivalent to Parallel.parSequenceVoid") {
     forAll { (es: SortedSet[Either[String, Int]]) =>
-      assert(Parallel.parSequence_[SortedSet, Either[String, *], Int](es) === (es.parSequence_))
+      assert(Parallel.parSequenceVoid[SortedSet, Either[String, *], Int](es) === es.parSequenceVoid)
     }
   }
 
@@ -105,9 +105,9 @@ class ParallelSuite
     }
   }
 
-  test("ParNonEmptyTraverse_ identity should be equivalent to parNonEmptySequence_") {
+  test("ParNonEmptyTraverseVoid identity should be equivalent to parNonEmptySequenceVoid") {
     forAll { (es: NonEmptyList[Either[String, Int]]) =>
-      assert(Parallel.parNonEmptyTraverse_(es)(identity) === (Parallel.parNonEmptySequence_(es)))
+      assert(Parallel.parNonEmptyTraverseVoid(es)(identity) === Parallel.parNonEmptySequenceVoid(es))
     }
   }
 
@@ -310,10 +310,10 @@ class ParallelSuite
     }
   }
 
-  test("ParReplicateA_ should be equivalent to fill parSequence_") {
+  test("ParReplicateA_ should be equivalent to fill parSequenceVoid") {
     forAll(Gen.choose(1, 20), Arbitrary.arbitrary[Either[String, String]]) {
       (repetitions: Int, e: Either[String, String]) =>
-        assert(Parallel.parReplicateA_(repetitions, e) === Parallel.parSequence_(List.fill(repetitions)(e)))
+        assert(Parallel.parReplicateA_(repetitions, e) === Parallel.parSequenceVoid(List.fill(repetitions)(e)))
     }
   }
 
diff --git a/tests/shared/src/test/scala/cats/tests/ReducibleSuite.scala b/tests/shared/src/test/scala/cats/tests/ReducibleSuite.scala
index 01dd07fd02..a17a44e443 100644
--- a/tests/shared/src/test/scala/cats/tests/ReducibleSuite.scala
+++ b/tests/shared/src/test/scala/cats/tests/ReducibleSuite.scala
@@ -234,11 +234,11 @@ abstract class ReducibleSuite[F[_]: Reducible](name: String)(implicit
     assert(out.toList === List(2, 4, 6, 9))
   }
 
-  test(s"Reducible[$name].nonEmptyTraverse_ can breakout") {
+  test(s"Reducible[$name].nonEmptyTraverseVoid can breakout") {
     val notAllEven = fromValues(2, 4, 6, 9, 10, 12, 14)
     val out = mutable.ListBuffer[Int]()
 
-    notAllEven.nonEmptyTraverse_ { a => out += a; if (a % 2 == 0) Some(a) else None }
+    notAllEven.nonEmptyTraverseVoid { a => out += a; if (a % 2 == 0) Some(a) else None }
 
     assert(out.toList === List(2, 4, 6, 9))
   }
diff --git a/tests/shared/src/test/scala/cats/tests/RegressionSuite.scala b/tests/shared/src/test/scala/cats/tests/RegressionSuite.scala
index b326f39c3b..2d852e2cb3 100644
--- a/tests/shared/src/test/scala/cats/tests/RegressionSuite.scala
+++ b/tests/shared/src/test/scala/cats/tests/RegressionSuite.scala
@@ -162,23 +162,23 @@ class RegressionSuite extends CatsSuite with ScalaVersionSpecificRegressionSuite
     assert(Vector(1, 2, 6, 8).traverse(validate) === (Either.left("6 is greater than 5")))
     checkAndResetCount(3)
 
-    assert(List(1, 2, 6, 8).traverse_(validate) === (Either.left("6 is greater than 5")))
+    assert(List(1, 2, 6, 8).traverseVoid(validate) === Either.left("6 is greater than 5"))
     checkAndResetCount(3)
 
     {
       @annotation.nowarn("cat=deprecation")
-      val obtained = Stream(1, 2, 6, 8).traverse_(validate)
+      val obtained = Stream(1, 2, 6, 8).traverseVoid(validate)
       assert(obtained === Either.left("6 is greater than 5"))
     }
     checkAndResetCount(3)
 
-    assert(Vector(1, 2, 6, 8).traverse_(validate) === (Either.left("6 is greater than 5")))
+    assert(Vector(1, 2, 6, 8).traverseVoid(validate) === Either.left("6 is greater than 5"))
     checkAndResetCount(3)
 
-    assert(NonEmptyList.of(1, 2, 6, 7, 8).traverse_(validate) === (Either.left("6 is greater than 5")))
+    assert(NonEmptyList.of(1, 2, 6, 7, 8).traverseVoid(validate) === Either.left("6 is greater than 5"))
     checkAndResetCount(3)
 
-    assert(NonEmptyList.of(6, 7, 8).traverse_(validate) === (Either.left("6 is greater than 5")))
+    assert(NonEmptyList.of(6, 7, 8).traverseVoid(validate) === Either.left("6 is greater than 5"))
     checkAndResetCount(1)
   }
 
diff --git a/tests/shared/src/test/scala/cats/tests/SyntaxSuite.scala b/tests/shared/src/test/scala/cats/tests/SyntaxSuite.scala
index 2f8e82e4bd..2b7f19277d 100644
--- a/tests/shared/src/test/scala/cats/tests/SyntaxSuite.scala
+++ b/tests/shared/src/test/scala/cats/tests/SyntaxSuite.scala
@@ -39,7 +39,6 @@ import cats.data.{
   ValidatedNec,
   ValidatedNel
 }
-import cats.syntax.OptionOps
 import cats.syntax.all._
 
 import scala.collection.immutable.{SortedMap, SortedSet}
@@ -155,11 +154,11 @@ object SyntaxSuite {
     val a1: A = fz.foldMap(f3)
 
     val f4 = mock[A => G[B]]
-    val gu0: G[Unit] = fa.traverse_(f4)
+    val gu0: G[Unit] = fa.traverseVoid(f4)
 
     val fga = mock[F[G[A]]]
-    val gu1: G[Unit] = fga.sequence_
-    val ga: G[A] = fga.foldK
+    val gu1: G[Unit] = fga.sequenceVoid // NestedFoldableOps
+    val ga1: G[A] = fga.foldK // NestedFoldableOps
 
     val f5 = mock[A => Boolean]
     val oa: Option[A] = fa.find(f5)
@@ -201,7 +200,19 @@ object SyntaxSuite {
     val gunit: G[F[A]] = fga.nonEmptySequence
   }
 
-  def testParallel[M[_]: Parallel, T[_]: Traverse, A, B]: Unit = {
+  def testParallelFoldable[M[_]: Parallel, T[_]: Foldable, A, B](): Unit = {
+    val ta = mock[T[A]]
+    val tma = mock[T[M[A]]]
+    val famb = mock[A => M[B]]
+
+    val mu1 = ta.parTraverseVoid(famb)
+    val mu2 = tma.parSequenceVoid
+
+    // Suppress "unused local val" warnings and make sure the types were inferred correctly.
+    val _ = (mu1: M[Unit], mu2: M[Unit])
+  }
+
+  def testParallelTraverse[M[_]: Parallel, T[_]: Traverse, A, B](): Unit = {
     val ta = mock[T[A]]
     val f = mock[A => M[B]]
     val mtb = ta.parTraverse(f)
@@ -348,7 +359,7 @@ object SyntaxSuite {
     val mtab2 = tmab.parLeftSequence
   }
 
-  def testParallelFoldable[T[_]: Foldable, M[_]: Parallel, A, B: Monoid]: Unit = {
+  def testParallelFoldableMonoid[T[_]: Foldable, M[_]: Parallel, A, B: Monoid](): Unit = {
     val ta = mock[T[A]]
     val f = mock[A => M[B]]
     val mb = ta.parFoldMapA(f)
@@ -379,9 +390,9 @@ object SyntaxSuite {
     val lb: Eval[B] = fa.reduceRightTo(f4)(f6)
 
     val f7 = mock[A => G[B]]
-    val gu1: G[Unit] = fa.nonEmptyTraverse_(f7)
+    val gu1: G[Unit] = fa.nonEmptyTraverseVoid(f7)
 
-    val gu2: G[Unit] = fga.nonEmptySequence_
+    val gu2: G[Unit] = fga.nonEmptySequenceVoid
   }
 
   def testFunctor[F[_]: Functor, A, B]: Unit = {
diff --git a/tests/shared/src/test/scala/cats/tests/TraverseSuite.scala b/tests/shared/src/test/scala/cats/tests/TraverseSuite.scala
index 94fffaea5e..1c6e8a1ad0 100644
--- a/tests/shared/src/test/scala/cats/tests/TraverseSuite.scala
+++ b/tests/shared/src/test/scala/cats/tests/TraverseSuite.scala
@@ -83,9 +83,9 @@ abstract class TraverseSuite[F[_]: Traverse](name: String)(implicit ArbFInt: Arb
     }
   }
 
-  test(s"Traverse[$name].traverse matches traverse_ with Option") {
+  test(s"Traverse[$name].traverse matches traverseVoid with Option") {
     forAll { (fa: F[Int], fn: Int => Option[Int]) =>
-      assert(Applicative[Option].void(fa.traverse(fn)) == fa.traverse_(fn))
+      assert(Applicative[Option].void(fa.traverse(fn)) == fa.traverseVoid(fn))
     }
   }