ABSTRACTMany animals exhibit social learning and behavioural traditions, but human culture exhibits unparalleled complexity and diversity, and is unambiguously cumulative in character. These similarities and differences have spawned a debate over whether animal traditions and human culture are reliant on homologous or analogous psychological processes. Human cumulative culture combines high‐fidelity transmission of cultural knowledge with beneficial modifications to generate a ‘ratcheting’ in technological complexity, leading to the development of traits far more complex than one individual could invent alone. Claims have been made for cumulative culture in several species of animals, including chimpanzees, orangutans andNewCaledonian crows, but these remain contentious. Whilst initial work on the topic of cumulative culture was largely theoretical, employing mathematical methods developed by population biologists, in recent years researchers from a wide range of disciplines, including psychology, biology, economics, biological anthropology, linguistics and archaeology, have turned their attention to the experimental investigation of cumulative culture. We review this literature, highlighting advances made in understanding the underlying processes of cumulative culture and emphasising areas of agreement and disagreement amongst investigators in separate fields.