Culture is increasingly being understood as a driver of mammalian phenotypes. Defined as group-specific behaviour transmitted by social learning, culture is shaped by social structure. However, culture can itself affect social structure if individuals preferentially interact with others whose behaviour is similar, or cultural symbols are used to mark groups. Using network formalism, this interplay can be depicted by the coevolution of nodes and edges together with the coevolution of network topology and transmission patterns. We review attempts to model the links between the spread, persistence and diversity of culture and the network topology of non-human societies. We illustrate these processes using cetaceans. The spread of socially learned begging behaviour within a population of bottlenose dolphins followed the topology of the social network, as did the evolution of the song of the humpback whale between breeding areas. In three bottlenose dolphin populations, individuals preferentially associated with animals using the same socially learned foraging behaviour. Homogeneous behaviour within the tight, nearly permanent social structures of the large matrilineal whales seems to result from transmission bias, with cultural symbols marking social structures. We recommend the integration of studies of culture and society in species for which social learning is an important determinant of behaviour.