This review is aimed at readers seeking an introductory overview, teaching courses and interested in visionary ideas. It first describes the range of topics covered by evolutionary medicine, which include human genetic variation, mismatches to modernity, reproductive medicine, degenerative disease, host–pathogen interactions and insights from comparisons with other species. It then discusses priorities for translational research, basic research and health management. Its conclusions are that evolutionary thinking should not displace other approaches to medical science, such as molecular medicine and cell and developmental biology, but that evolutionary insights can combine with and complement established approaches to reduce suffering and save lives. Because we are on the cusp of so much new research and innovative insights, it is hard to estimate how much impact evolutionary thinking will have on medicine, but it is already clear that its potential is enormous.