Why species are found where they are is a central question in biogeography. The most widely used tool for understanding the controls on distribution is species distribution modelling. Species distribution modelling is now a well-established method in both the theoretical and applied ecological literature. In this special issue we examine the current state of the art in species distribution modelling and explore avenues for including more biological processes in such models. In particular we focus on physiological, demographic, dispersal, competitive and ecological-modulation processes. This overview highlights opportunities for new species distribution model concepts and developments, as well as a statistical agenda for implementing such models.