Overview Evolutionary game theory may have done more to stimulate and refine research in animal behaviour than any other theoretical perspective. In this chapter, we will review some of the insights gained by applying game theory to animal behaviour. Our emphasis is on conceptual issues rather than on technical detail. We start by introducing some of the classical models, including the Hawk–Dove game and the Prisoner's Dilemma game. Then we discuss in detail the main ingredients of a game-theoretical approach: strategies, payoffs and ‘solution concepts’ such as evolutionary stability. It should become clear that first-generation models like the Hawk–Dove game, while of enormous conceptual importance, have severe limitations when applied to real-world scenarios. We close with a sketch of what we see as the most important gaps in our knowledge, and the most relevant current developments in evolutionary game theory. Introduction Social behaviour involves the interaction of several individuals. Therefore within most social contexts the best thing to do depends on what others are doing. In other words, within social contexts selection is typically frequency-dependent (Ayala & Campbell 1974, Heino et al. 1998). Game theory was originally formulated to predict behaviour when there is frequency dependence in economics, for example competition between firms (von Neumann & Morgenstern 1944, Luce & Raiffa 1957).