Natural landscapes are often not homogeneous but show spatial variation in environmental conditions. Natural and human disturbances result in additional landscape fragmentation and heterogeneity. In this talk, I will consider (a) conditions under which species can survive in such fragmented landscapes, (b) velocities of species invasion, and (c) effect of heterogeneity on competition between two species. I will consider these questions in discrete-time models formulated as integrodifference equations. I will present various approximation techniques to deal with spatial heterogeneity.