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The paleontologists thought that ancient whales were members of an extinct group of highly-specialized ungulates (hoofed mammals) called mesonychians. Mesonychians were meat eaters and ranged in size from the size of weasels to grizzly bears. The most important evidence was in the similarities in the cranial and dental morphologies of mesonychians and cetaceans. Molecular biologists favored artiodactyls (even-toed ungulates such as cows, pigs, camels, deer, and hippos) as the ancestors of cetaceans. These scientists said cetaceans are a sister group to hippos because they share more DNA than do whales with any other land mammal.

Apparently that's what they used to think. Now they think whales evolved from hippo-like animals.Read the whole story

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The currently favored hypothesis is this: cetaceans were descended from a very early, as yet unknown artiodactyl. This artiodactyls had a slightly more primitive ankle structure than any known artiodactyls. It was also more primitive than the known ancestor of hippos, the anthracotherioids. Therefore, the cetaceans separated from the artiodactyls and anthracotherioids before the Eocene.

Of course, any hypothesis that's based on fossils that are tens of millions of years old is bound to have problems. The similarity in cetacean and mesonychian cranial and dental morphology becomes a question. Was this the result of convergent evolution or was it a feature that was shared by a very early common ancestor to the three groups (cetaceans, mesonychians, and artiodactyls) but was lost in later artiodactyls? Also, the DNA analysis favors a sister-group relationship between whales and hippos but, morphologically, hippos are closer to artiodactyls than whales. Therefore, the relationship between whales and hippos remains unclear. The answers will likely come from as-yet-undiscovered fossil finds.