<p>Cyber–physical–human systems (CPHSs) — characterized by the organic integration of physical components, a computation and communication cyber layer, and humans — are becoming an integral part of daily life, with applications ranging from assistive robots to smart buildings and modern logistics systems. The key role of humans in these complex systems calls for a paradigm shift, from classical machine-oriented control methods to approaches that focus on the explicit modelling and control of the human layer of a CPHS. In this Review, we showcase state-of-the-art research in mathematical modelling and control of CPHSs. We discuss established control-theoretic approaches to model and control cyber–physical systems, explore two mathematical approaches to modelling human behaviour and social influence, utilizing tools from game theory and opinion dynamics, and show how these models are integrated into CPHSs. Moving to control, we focus on the potential and the challenges that are associated with the human layer. We present approaches for control on different layers, paying attention to the fact that humans can typically only be guided or nudged, and then discuss control across layers. Finally, we describe some major open questions in controlling CPHSs, including integrating data-driven approaches and bridging the gap between theoretical and experimental studies.</p>