The arrival of farming in Europe beginning around 8,500 years ago required adaptation to new environments, pathogens, diets, and social organizations. While evidence of natural selection can be revealed by studying patterns of genetic variation in present-day people, these pattern are only indirect echoes of past events, and provide little information about where and when selection occurred. Ancient DNA makes it possible to examine populations as they were before, during and after adaptation events, and thus to reveal the tempo and mode of selection. Here we report the first genome-wide scan for selection using ancient DNA, based on 83 human samples from Holocene Europe analyzed at over 300,000 positions. We find five genome-wide signals of selection, at loci associated with diet and pigmentation. Surprisingly in light of suggestions of selection on immune traits associated with the advent of agriculture and denser living conditions, we find no strong sweeps associated with immunological phenotypes. We also report a scan for selection for complex traits, and find two signals of selection on height: for short stature in Iberia after the arrival of agriculture, and for tall stature on the Pontic-Caspian steppe earlier than 5,000 years ago. A surprise is that in Scandinavian hunter-gatherers living around 8,000 years ago, there is a high frequency of the derived allele at the EDAR gene that is the strongest known signal of selection in East Asians and that is thought to have arisen in East Asia. These results document the power of ancient DNA to reveal features of past adaptation that could not be understood from analyses of present-day people.