The past few years have witnessed a revolution in our ability to obtain DNA from ancient humans. This important new data has added to our knowledge from archaeology and anthropology, helped resolve long-existing controversies, challenged long-held views, and thrown up remarkable surprises. The emerging picture is one of many waves of ancient human migrations, so that all populations living today are mixes of ancient ones, and often carry a genetic component from archaic humans. David Reich, whose team has been at the forefront of these discoveries, explains what genetics is telling us about ourselves and our complex and often surprising ancestry. Gone are old ideas of any kind of racial apurity.’ Instead, we are finding a rich variety of mixtures. Reich describes the cutting-edge findings from the past few years, and also considers the sensitivities involved in tracing ancestry, with science sometimes jostling with politics and tradition. He brings an important wider message: that we should recognize that every one of us is the result of a long history of migration and intermixing of ancient peoples, which we carry as ghosts in our DNA. What will we discover next?