We develop a conceptual framework for studying collective adaptation in complex socio-cognitive systems, driven by dynamic interactions of social integration strategies, social environments and problem structures. Going beyond searching for 'intelligent' collectives, we integrate research from different disciplines and outline modelling approaches that can be used to begin answering questions such as why collectives sometimes fail to reach seemingly obvious solutions, how they change their strategies and network structures in response to different problems and how we can anticipate and perhaps change future harmful societal trajectories. We discuss the importance of considering path dependence, lack of optimization and collective myopia to understand the sometimes counterintuitive outcomes of collective adaptation. We call for a transdisciplinary, quantitative and societally useful social science that can help us to understand our rapidly changing and ever more complex societies, avoid collective disasters and reach the full potential of our ability to organize in adaptive collectives.