We discuss the apparent paradox that while introduced populations often adapt rapidly to conditions in the new range, it is normally assumed that the species' niche remains unchanged. Focusing on plants, we argue that studies of the niche dynamics of alien species are useful for understanding the constraints acting on species in their native ranges, and vice versa. Most hypotheses about species ecological range margins are more consistent with there being a niche shift than niche stasis in the new range. After reviewing the evidence for niche shifts in alien species, we suggest that the probability of a shift occurring depends primarily upon the ecological and genetic processes limiting the species in its native range. For example, a fundamental niche shift might occur if introduced individuals are released from maladaptive gene flow from central populations, or if genetic diversity is increased by the mixing of individuals from different sources. In addition, other factors such as species characteristics, introduction history and conditions in the new range may also influence whether a niche shift occurs. Based on these considerations, we propose conditions under which niche shifts are most likely. Such understanding is important for predicting and mitigating current and future anthropogenic impacts on species ranges.