Abstract: Animal populations often self-organize into territorial structure from movements and interactions of individual animals. Spatial memory is one of cognitive processes that may affect the movement and navigation of the animals. We will review several mathematical approaches of animal spatial movements: (i) reaction-diffusion-advection model with time-delayed memory-based movement; and (ii) reaction-diffusion-advection model with a non-local advection term driven by a cognitive map representing memory of past animal locations embedded in the environment. The well-posedness of models and bifurcation of spatiotemporal patterns will be discussed.