We have known for decades (Payne and McVay, 1971) that cetaceans communicate with each other. A variety of languages and dialects have been discovered, graphed and analyzed. Researchers have surmised what these vocalizations mean. They have also confirmed that these sounds are separate from the sounds that odontocetes (toothed whales) make to hunt and navigate. A recently published paper in Current Biology posits that at least one species, the beluga (Delphinapterus leucas) has the ability to mimic human sounds. Here are links to a couple of articles that have been written: Boston Globe, and Huffington Post.
Belugas already have the distinction of having the most demonstrative face in the whale world and are one of the few species to not have any of its neck vertebrae fused together. Now they appear to be able to mimic human language. Dory and Marlin (from Finding Nemo) would be proud.