The main purpose of this talk is to answer the question of how the species’ dispersal strategies among different habitats affect on its survival. We develop two patchy predator-prey models: First, we propose a general predator-pry dispersal model and obtain its threshold dynamics determined by the net reproductive number, based on which we discuss the effects of predator dispersal strategies on its persistence & extinction; Second, we consider a specific dispersal model where only the predator migrates, we construct the global stability of its coexistence equilibrium and investigate the effects of dispersal strategies on the amount of predator population. The talk is based on joint works with Xuejuan Lu and Yuming Chen.