The 'social complexity hypothesis' for communication posits that groups with complex social systems require more complex communicative systems to regulate interactions and relations among group members. Complex social systems, compared with simple social systems, are those in which individuals frequently interact in many different contexts with many different individuals, and often repeatedly interact with many of the same individuals in networks over time. Complex communicative systems, compared with simple communicative systems, are those that contain a large number of structurally and functionally distinct elements or possess a high amount of bits of information. Here, we describe some of the historical arguments that led to the social complexity hypothesis, and review evidence in support of the hypothesis. We discuss social complexity as a driver of communication and possible causal factor in human language origins. Finally, we discuss some of the key current limitations to the social complexity hypothesis-the lack of tests against alternative hypotheses for communicative complexity and evidence corroborating the hypothesis from modalities other than the vocal signalling channel.