Over the past decade, a major debate has taken place on the underpinnings of cultural changes in human societies. A growing array of evidence in behavioural and evolutionary biology has revealed that social connectivity among populations and within them affects, and is affected by, culture. Yet the interplay between prehistoric hunter–gatherer social structure and cultural transmission has typically been overlooked. Interestingly, the archaeological record contains large data sets, allowing us to track cultural changes over thousands of years: they thus offer a unique opportunity to shed light on long‐term cultural transmission processes. In this review, we demonstrate how well‐developed methods for social structure analysis can increase our understanding of the selective pressures underlying cumulative culture. We propose a multilevel analytical framework that considers finer aspects of the complex social structure in which regional groups of prehistoric hunter–gatherers were embedded. We put forward predictions of cultural transmission based on local‐ and global‐level network metrics of small‐scale societies and their potential effects on cumulative culture. By bridging the gaps between network science, palaeodemography and cultural evolution, we draw attention to the use of the archaeological record to depict patterns of social interactions and transmission variability. We argue that this new framework will contribute to improving our understanding of social interaction patterns, as well as the contexts in which cultural changes occur. Ultimately, this may provide insights into the evolution of human behaviour.