Consistent individual differences in animal behaviour are an increasingly common focus of research across various behavioural and biological sciences. Such ‘animal personalities’ comprise a diverse repertoire of behavioural tendencies, recently expanding to incorporate the social domain. Aggression and peace, hallmarks of many social systems including that of humans, warrant integration with this literature. Specifically, animal personality research should consider the potential role of stable conflict and post-conflict behavioural tendencies. We focus our discussion primarily on examples in nonhuman primates and humans, but suggest that individual variation patterns are relevant for any social species in which these phenomena exist. In highly gregarious species, an individual’s conflict and post-conflict tendencies can affect the strength and stability of its social bonds. Because social relationships in turn impact survival and reproductive success, we also encourage future work to investigate the ultimate (i.e., fitness-relevant) consequences of individual variation in aggressive and peaceful behaviour.