Limits to evolution at range margins: when and why does adaptation fail?

What stops populations expanding into new territory beyond the edge of a range margin? Recent models addressing this problem have brought together population genetics and population ecology, and some have included interactions among species at range edges. Here, we review these models of adaptation at environmental or parapatric margins, and discuss the contrasting effects of migration in either swamping local adaptation, or supplying the genetic variation that is necessary for adaptation to continue. We illustrate how studying adaptation at range margins (both with and without hybridization) can provide insight into the genetic and ecological factors that limit evolution more generally, especially in response to current rates of environmental change.