The arrival of an invasive species can have wide-ranging ecological impacts on native taxa, inducing rapid evolutionary responses in ways that either reduce the invader’s impact or exploit the novel opportunity that it provides. The invasion process itself can cause substantial evolutionary shifts in traits that influence the invader’s dispersal rate (via both adaptive and non-adaptive mechanisms) and its ability to establish new populations. I briefly review the nature of evolutionary changes likely to be set in train by a biological invasion, with special emphasis on recent results from my own research group on the invasion of cane toads (Rhinella marina) through tropical Australia. The toads’ invasion has caused evolutionary changes both in the toads and in native taxa. Many of those changes are adaptive, but others may result from non-adaptive evolutionary processes: for example, the evolved acceleration in toad dispersal rates may be due to spatial sorting of dispersal-enhancing genes, rather than fitness advantages to faster-dispersing individuals. Managers need to incorporate evolutionary dynamics into their conservation planning, because biological invasions can affect both the rates and the trajectories of evolutionary change.