Most evolutionary theory does not deal with populations expanding or contracting in space. Invasive species, climate change, epidemics, and the breakdown of dispersal barriers, however, all create populations in this kind of spatial disequilibrium. Importantly, spatial disequilibrium can have important ecological and evolutionary outcomes. During continuous range expansion, for example, populations on the expanding front experience novel evolutionary pressures because frontal populations are assorted by dispersal ability and have a lower density of conspecifics than do core populations. These conditions favor the evolution of traits that increase rates of dispersal and reproduction. Additionally, lowered density on the expanding front eventually frees populations on the expanding edge from specialist, coevolved enemies, permitting higher investment into traits associated with dispersal and reproduction rather than defense against pathogens. As a result, the process of range expansion drives rapid life-history evolution, and this seems to occur despite ongoing serial founder events that have complex effects on genetic diversity at the expanding front. Traits evolving on the expanding edge are smeared across the landscape as the front moves through, leaving an ephemeral signature of range expansion in the life-history traits of a species across its newly colonized range. Recent studies suggest that such nonequilibrium processes during recent population history may have contributed to many patterns usually ascribed to evolutionary forces acting in populations at spatial equilibrium.