  Territorial behaviour is widespread in the animal kingdom, with creatures
seeking to gain parts of space for their exclusive use. It arises through a
complicated interplay of many different behavioural features. Extracting and
quantifying the processes that give rise to territorial patterns requires both
mathematical models of movement and interaction mechanisms, together with
statistical techniques for rigorously extracting parameters from data. Here, we
give a brisk, pedagogical overview of the techniques so far developed to tackle
the problem of territory formation. We give some examples of what has already
been achieved using these techniques, together with pointers as to where we
believe the future lies in this area of study. This progress is a single
example of a major aim for 21st century science: to construct quantitatively
predictive theory for ecological systems.
