There is great interest in environmental effects on the development and evolution of animal personality traits. An important component of an individual's environment is its social environment. However, few studies look beyond dyadic relationships and try to place the personality of individuals in the context of a social network. Social network analysis provides us with many new metrics to characterize the social fine-structure of populations and, therefore, with an opportunity to gain an understanding of the role that different personalities play in groups, communities and populations regarding information or disease transmission or in terms of cooperation and policing of social conflicts. The network position of an individual is largely a consequence of its interactive strategies. However, the network position can also shape an individual's experiences (especially in the case of juveniles) and therefore can influence the way in which it interacts with others in future. Finally, over evolutionary time, the social fine-structure of animal populations (as quantified by social network analysis) can have important consequences for the evolution of personalities—an approach that goes beyond the conventional game-theoretic analyses that assumed random mixing of individuals in populations.