Abstract: The social brain hypothesis was proposed as an explanation for the fact that primates have unusually large brains for body size compared to all other vertebrates: Primates evolved large brains to manage their unusually complex social systems. Although this proposal has been generalized to all vertebrate taxa as an explanation for brain evolution, recent analyses suggest that the social brain hypothesis takes a very different form in other mammals and birds than it does in anthropoid primates. In primates, there is a quantitative relationship between brain size and social group size (group size is a monotonic function of brain size), presumably because the cognitive demands of sociality place a constraint on the number of individuals that can be maintained in a coherent group. In other mammals and birds, the relationship is a qualitative one: Large brains are associated with categorical differences in mating system, with species that have pairbonded mating systems having the largest brains. It seems that anthropoid primates may have generalized the bonding processes that characterize monogamous pairbonds to other non-reproductive relationships (?friendships?), thereby giving rise to the quantitative relationship between group size and brain size that we find in this taxon. This raises issues about why bonded relationships are cognitively so demanding (and, indeed, raises questions about what a bonded relationship actually is), and when and why primates undertook this change in social style.