Game Theory has been developed as a theory of rational behavior in interpersonal conflict situations, with economics and the other social sciences being the intended fields of application. Since the theory is based on an idealized picture of human rationality, it is by no means obvious that it can be applied to situations in which the players cannot be attributed any intellectual capabilities. However, in their seminal paper ‘The logic of animal conflict’, Maynard Smith and Price showed that animal contests can be modeled as games and that game theory can be applied successfully in biology. The objective of this chapter is to review some of the developments in this biological branch of Game Theory and to point out the distinctions and similarities with the classical branch (also see Parker and Hammerstein [1985] ). The main emphasis will be on the mathematics involved, lack of space prevents an extensive discussion of the underlying biological assumptions as well as an analysis of specific examples. For these, the reader is referred to the very stimulating book ‘Evolution and the Theory of Games’ by John Maynard Smith.