Behavioural adaptation of farm animals to environmental changes contributes to high levels of production under a wide range of farming conditions, from highly controlled indoor systems to harsh outdoor systems. The genetic variation in livestock behaviour is considerable. Animals and genotypes with a larger behavioural capacity for adaptation may cope more readily with varying farming conditions than those with a lower capacity for adaptation. This capacity should be exploited when the aim is to use a limited number of species extensively across the world. The genetics of behavioural traits is understood to some extent, but it is seldom accounted for in breeding programmes. This review summarizes the estimates of genetic parameters for behavioural traits in cattle, pigs, poultry and fish. On the basis of the major studies performed in the last two decades, we focus the review on traits of common interest in the four species. These concern the behavioural responses to both acute and chronic stressors in the physical environment (feed, temperature, etc.) and those in the social environment (other group members, progeny, humans). The genetic strategies used to improve the behavioural capacity for adaptation of animals differ between species. There is a greater emphasis on responses to acute environmental stress in fish and birds, and on responses to chronic social stress in mammals.