1. The social decisions that individuals make, in terms of where to move, who to interact with and how frequently, scale up to generate social structure. Such structure has profound consequences: individuals each have a unique social environment, social interactions can amplify or dampen individual differences at the population level, and population-level ecological and evolutionary processes can be governed by higher-level ‘emergent properties’ of animal societies. 2. Here we review how explicitly accounting for social structure in animal populations has generated new hypotheses and has revised existing predictions in ecology and evolution. That is, we synthesize the insights gained by applying ‘network-thinking’ rather than the utility of applying social network analysis as a methodological tool. 3. We start with what has been learned about the generative mechanisms that underpin social structure. We then outline the major implications that social structure has been found to have on population processes, on how selection operates and organisms can evolve, and on co-evolutionary dynamics between social structure and population processes. Finally, we highlight areas for which there is clear evidence that accounting for social structure will refine current thinking, but where examples remain scarce. 4. Applying ‘network thinking’ in biology presents not only new challenges, but also many opportunities to advance different areas of research. Addressing the question of how social structure changes the biological relationships linking individuals to populations, and populations to processes, is revealing commonalities across scientific disciplines. In doing so, animal social networks can bridge otherwise disparate research topics and, in the future, we hope will allow for more unified theories in biology.