Spotted hyenas (Crocuta crocuta) are large mammalian carnivores, but their societies, called ‘clans’, resemble those of such cercopithecine primates as baboons and macaques with respect to their size, hierarchical structure, and frequency of social interaction among both kin and unrelated group-mates. However, in contrast to cercopithecine primates, spotted hyenas regularly hunt antelope and compete with group-mates for access to kills, which are extremely rich food sources, but also rare and ephemeral. This unique occurrence of baboon-like sociality among top-level predators has favoured the evolution of many unusual traits in this species. We briefly review the relevant socio-ecology of spotted hyenas, document great demographic variation but little variation in social structure across the species’ range, and describe the long-term fitness consequences of rank-related variation in resource access among clan-mates. We then summarize patterns of genetic relatedness within and between clans, including some from a population that had recently gone through a population bottleneck, and consider the roles of sexually dimorphic dispersal and female mate choice in the generation of these patterns. Finally, we apply social network theory under varying regimes of resource availability to analyse the effects of kinship on the stability of social relationships among members of one large hyena clan in Kenya. Although social bonds among both kin and non-kin are weakest when resource competition is most intense, hyenas sustain strong social relationships with kin year-round, despite constraints imposed by resource limitation. Our analyses suggest that selection might act on both individuals and matrilineal kin groups within clans containing multiple matrilines.