Ancient DNA makes it possible to directly witness natural selection by analyzing samples from populations before, during and after adaptation events. Here we report the first scan for selection using ancient DNA, capitalizing on the largest genome-wide dataset yet assembled: 230 West Eurasians dating to between 6500 and 1000 BCE, including 163 with newly reported data. The new samples include the first genome-wide data from the Anatolian Neolithic culture whose genetic material we extracted from the DNA-rich petrous bone and who we show were members of the population that was the source of Europe’s first farmers. We also report a complete transect of the steppe region in Samara between 5500 and 1200 BCE that allows us to recognize admixture from at least two external sources into steppe populations during this period. We detect selection at loci associated with diet, pigmentation and immunity, and two independent episodes of selection on height.