The field of collective animal behaviour examines how relatively simple, local interactions between individuals in groups combine to produce global-level outcomes. Existing mathematical models and empirical work have identified candidate mechanisms for numerous collective phenomena, but have typically focused on one-off or short-term performance. We argue that feedback between collective performance and learning – giving the former the capacity to become an adaptive, and potentially cumulative, process – is a currently poorly explored, but crucial mechanism in understanding collective systems. We synthesise material ranging from swarm intelligence in social insects, through collective movements in vertebrates, to collective decision-making in animal and human groups, to propose avenues for future research to identify the potential for changes in these systems to accumulate over time.