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Genome-wide computational studies can now identify targets of natural selection. The unique information about humans these studies reveal, and the media attention they attract, indicate the need for caution and precision in communicating results. This need is exacerbated by ways in which evolutionary and genetic considerations have been misapplied to support discriminatory policies, by persistent misconceptions of these fields and by the social sensitivity surrounding discussions of racial ancestry. We discuss the foundations, accomplishments and future directions of human evolutionary genomics, attending to ways in which the interpretation of good science can go awry, and offer suggestions for researchers to prevent misapplication of their work.