Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on extensions of simple random walk processes. In this talk I will review some of the basic ideas behind the theory of random walks and diffusion processes and discuss how these models are used in the context of modelling animal movement. I will present several case studies, each of which is an extension or application of some of the simple random walk ideas discussed previously. Specifically, I will consider problems related to biased and correlated movements, path analysis of movement data, sampling and processing issues and the problem of determining movement processes from observed patterns. I will also discuss some biological examples of how these models can be used, including chemosensory movements and interactions between zooplankton and the movements of fish.
