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A central question in the study of the evolution of dispersal is what kind of dispersal strategies are evolutionary stable. Hastings showed that among unconditional dispersal strategies in a spatially heterogeneous but temporally constant environment, the dispersal strategy with no movement is convergent stable. McPeek and Holt’s work suggested that among conditional dispersal strategies in a spatially heterogeneous but temporally constant environment, an ideal free dispersal strategy, which results in the ideal free distribution for a single species at equilibrium, is evolutionary stable. We use continuoustime and discrete-space models to determine when the dispersal strategy with no movement is evolutionary stable and when an ideal dispersal strategy is evolutionary stable, both in a spatially heterogeneous but temporally constant environment. Nonlocal dispersal will also be discussed if time allows. This is a joint work with Steve Cantrell and Chris Cosner, University of Miami.