The past few years have seen a revolution in our ability to map whole genome DNA from ancient humans. With the ancient DNA revolution, combined with rapid genome mapping of present human populations, has come remarkable insights into our past. This important new data has clarified and added to our knowledge from archaeology and anthropology, helped resolve long-existing controversies, challenged long-held views, and thrown up some remarkable surprises. The emerging picture is one of many waves of ancient human migrations, so that all populations existing today are mixes of ancient ones, as well as in many cases carrying a genetic component from Neanderthals, and, in some populations, Denisovans. David Reich, whose team has been at the forefront of these discoveries, explains what the genetics is telling us about ourselves and our complex and often surprising ancestry. Gone are old ideas of any kind of racial ‘purity’, or even deep and ancientdivides