Genetic information contains a record of the history of our species, and technological advances have transformed our ability to access this record. Many studies have used genome-wide data from populations today to learn about the peopling of the globe and subsequent adaptation to local conditions. Implicit in this research is the assumption that the geographic locations of people today are informative about the geographic locations of their ancestors in the distant past. However, it is now clear that long-range migration, admixture and population replacement have been the rule rather than the exception in human history. In light of this, we argue that it is time to critically re-evaluate current views of the peopling of the globe and the importance of natural selection in determining the geographic distribution of phenotypes. We specifically highlight the transformative potential of ancient DNA. By accessing the genetic make-up of populations living at archaeologically-known times and places, ancient DNA makes it possible to directly track migrations and responses to natural selection.