Aim: Ongoing climate change is currently modifying the geographical location of areas that are climatically suitable for species. Understanding a species ability to successfully shift its geographical range would allow us to assess extinction risks and predict future community compositions. We investigate how habitat configuration impedes or promotes climate-driven range shifts, given different speeds of climate change and dispersal abilities. Location: Theoretical, but illustrated with European examples. Methods: We model how a species ability to track a directional shift in climatic conditions is affected by (a) species dispersal abilities; (b) speed of climatic shift; and (c) spatial arrangement of the habitat. Our modelling framework includes within-and between-patch population dynamics and uses ecologically realistic habitat distributions and dispersal scenarios (verified with data from a set of European mammal species) and, as such, is an improvement of classical range shift models. Result: In landscapes with a homogeneous distribution of suitable habitats, all but the least dispersive species will be able to range shift. However, species with high dispersal ability will have lower population densities after range shift. In heterogeneous landscapes species ability to range shift is far more variable and heavily dependent on the habitat configuration. This means that landscape configuration in combination with the speed of climate change and species dispersal abilities give rise to nonlinear effects on population sizes and survival after a climatic shift. Main conclusions: Our analyses point out the importance of accounting for the interplay of species dispersal and the landscape configuration when estimating future climate impact on species. These results link ecologically important attributes of both species and their landscapes to outcomes of species range shift, and thereby long-term persistence of ecological communities.