Aggression (behaviour that actually or potentially causes harm to another animal) is widespread among fishes, often taking the form of territoriality or dominance. The mechanisms that control aggression in fish are described, including the effects of stimuli from opponents, the importance of the context in which an aggressive encounter occurs and the effects of nutritional condition, endocrine status and brain biochemistry. The way aggression changes during development is then considered, evidence given for inherited differences in aggressiveness and an account presented of the environmental factors that influence the way aggression develops. The benefits that fish gain from winning fights, the costs that they incur from fighting and how they balance costs against benefits to promote their individual fitness are described. Data are then given on the incidence of aggression among cultured fish, on some resulting problems for production, welfare and environmental protection and on the effects of domestication and captive rearing of aggressiveness. Possible solutions to such problems are discussed, based on selecting appropriate fish for culture and the design of husbandry systems that minimise aggression. Finally, some systems for mitigating the effects of domestication and captive rearing on the aggressive behaviour of cultured fish are described.