For many species, human-induced environmental changes are important indirect drivers of range expansion into new regions. We argue that it is important to distinguish the range dynamics of such species from those that occur without, or with less clear, involvement of human-induced environmental changes. We elucidate the salient features of the rapid increase in the number of species whose range dynamics are human induced, and review the relationships and differences to both natural range expansion and biological invasions. We discuss the consequences for science, policy and management in an era of rapid global change and highlight four key challenges relating to basic gaps in knowledge, and the transfer of scientific understanding to biodiversity management and policy. We conclude that range-expanding species responding to human-induced environmental change will become an essential feature for biodiversity management and science in the Anthropocene. Finally, we propose the term neonative for these taxa.