Ancestry connects genetics and society in fundamental ways. For many people it has cultural, religious or even political significance, and can play a key role in shaping personal and public identities. People’s desire to discover their own ancestry drives the multibillion-dollar genealogy industry, which has grown rapidly in the era of consumer genomics. Companies such as 23andMe and Ancestry now claim tens of millions of customers worldwide. In parallel, our scientific understanding of the human past is being transformed by studies of ancient and modern genetic data, which allow us to track changes in ancestry over space and time. Sophisticated methods have been developed to infer and visualise these relationships. Thus, it seems that both scientists and the wider public are learning more and more about ancestry, and there is an optimistic sense that genetic data provide an exhaustive repository of ancestral information.