Within animal populations there is variation among individuals in their tendency to be social, where more sociable individuals associate more with other individuals. Consistent inter‐individual variation in ‘sociability’ is considered one of the major axes of personality variation in animals along with aggressiveness, activity, exploration and boldness. Not only is variation in sociability important in terms of animal personalities, but it holds particular significance for, and can be informed by, two other topics of major interest: social networks and collective behaviour. Further, knowledge of what generates inter‐individual variation in social behaviour also holds applied implications, such as understanding disorders of social behaviour in humans. In turn, research using non‐human animals in the genetics, neuroscience and physiology of these disorders can inform our understanding of sociability. For the first time, this review brings together insights across these areas of research, across animal taxa from primates to invertebrates, and across studies from both the laboratory and field. We show there are mixed results in whether and how sociability correlates with other major behavioural traits. Whether and in what direction these correlations are observed may differ with individual traits such as sex and body condition, as well as ecological conditions. A large body of evidence provides the proximate mechanisms for why individuals vary in their social tendency. Evidence exists for the importance of genes and their expression, chemical messengers, social interactions and the environment in determining an individual's social tendency, although the specifics vary with species and other variables such as age, and interactions amongst these proximate factors. Less well understood is how evolution can maintain consistent variation in social tendencies within populations. Shifts in the benefits and costs of social tendencies over time, as well as the social niche hypothesis, are currently the best supported theories for how variation in sociability can evolve and be maintained in populations. Increased exposure to infectious diseases is the best documented cost of a greater social tendency, and benefits include greater access to socially transmitted information. We also highlight that direct evidence for more sociable individuals being safer from predators is lacking. Variation in sociability is likely to have broad ecological consequences, but beyond its importance in the spread of infectious diseases, direct evidence is limited to a few examples related to dispersal and invasive species biology. Overall, our knowledge of inter‐individual variation in sociability is highly skewed towards the proximate mechanisms. Our review also demonstrates, however, that considering research from social networks and collective behaviour greatly enriches our understanding of sociability, highlighting the need for greater integration of these approaches into future animal personality research to address the imbalance in ou...