The phenomenon of kleptoparasitism - "food-stealing" - has frequently been observed, in a wide range of animal species. In this thesis, I extend the game-theoretic model of kleptoparasitism, proposed by Broom and Ruxton 1998, in a number of ways. Firstly, using their model, I investigate how quickly the equilibrium state of a kleptoparasitic population is reached. This work has been published (Luther and Broom 2004). I then investigate the case of a single homogenous population of kleptoparasites, finding which behaviours are Evolutionarily Stable Strategies. This is done with a variable probability that a challenger succeeds when attempting to steal food from a handler, and also allowing the possibility that the handler does not resist the attack. This work has been published (Broom et al 2004) I then consider populations of two groups, one stealing and the other only foraging, to find ESS's, particularly looking at situations where a mixed population can be an ESS, and other cases where pure populations are an ESS. I do this for indistinguishable groups, and then distinguishable groups. I show that a homogenous facultative population behaving in the Broom and Ruxton 1998 ESS has the same handling ratio as a mixed obligate population of kleptoparasites and foragers. Finally, I discuss some ornithological data on kleptoparasitism, and make a simple comparison with our models, to see if they are an accurate representation of the actual phenomenon