Humans have dramatic, diverse and far-reaching influences on the evolution of other organisms. Numerous examples of this human-induced contemporary evolution have been reported in a number of 'contexts', including hunting, harvesting, fishing, agriculture, medicine, climate change, pollution, eutrophication, urbanization, habitat fragmentation, biological invasions and emerging/disappearing diseases. Although numerous papers, journal special issues and books have addressed each of these contexts individually, the time has come to consider them together and thereby seek important similarities and differences. The goal of this special issue, and this introductory paper, is to promote and expand this nascent integration. We first develop predictions as to which human contexts might cause the strongest and most consistent directional selection, the greatest changes in evolutionary potential, the greatest genetic (as opposed to plastic) changes and the greatest effects on evolutionary diversification We then develop predictions as to the contexts where human-induced evolutionary changes might have the strongest effects on the population dynamics of the focal evolving species, the structure of their communities, the functions of their ecosystems and the benefits and costs for human societies. These qualitative predictions are intended as a rallying point for broader and more detailed future discussions of how human influences shape evolution, and how that evolution then influences species traits, biodiversity, ecosystems and humans.This article is part of the themed issue 'Human influences on evolution, and the ecological and societal consequences'.