build.sbt

name:="futures-test"

scalaVersion:="2.11.7"

libraryDependencies += "org.scalatest" %% "scalatest" % "2.2.5"

ExampleCode.scala

package future_test

import scala.concurrent.{ExecutionContext, Future}

object ExampleCode {
  def execute()(implicit ec: ExecutionContext): Future[String] = {
    Future { throw new TestException("Some data") }
  }
}

class TestException(data: String) extends RuntimeException("Expected in test")

ExampleTest.scala

package future_test

import org.scalatest.concurrent.ScalaFutures
import org.scalatest.{ShouldMatchers, WordSpec}

class ExampleTest extends WordSpec with ShouldMatchers with ScalaFutures{
  import scala.concurrent.ExecutionContext.Implicits.global
  ".futureValue when Future contains an exception" should {
    "allow to test on that exception class" in {
      a[TestException] should be thrownBy(ExampleCode.execute().futureValue)
    }
    "allow to test on RuntimeException" in {
      ExampleCode.execute().futureValue
    }
  }
}

futureValue warps exceptions as TestFailedException
see https://gist.github.com/maowug/b0e3f564fc9c6290f3367a6650d194d2