In this talk I shall discuss the physiology of cognitive control. One classical approach seeks abstract control functions (e.g. inhibition, set switching), perhaps associated with specific coarse regions of the frontal lobe. I suggest that this way of posing the problem is mistaken. Behaviour is directed by a whole-brain model of the current situation, with many parts integrated into their correct roles and relationships. At the heart of this integration is a multiple-demand (MD) system well known from human brain imaging, with components closely connected, but widely distributed across the cortex. To address physiology, I shall discuss neural data from monkeys solving problems in an on-screen maze. With recordings from four putative homologues to human MD regions, in different regions of the frontal lobe, we examine key components of a mental model – current state, goal state, actions diminishing the difference between these two, and abstract problem structure. Across regions there was overlap but also wide quantitative variation in encoding fundamental task features. Sensory input and current state were strongly coded in ventrolateral frontal cortex, goal most stably in dorsomedial frontal cortex, and move most rapidly in both ventrolateral and dorsal premotor cortex. Insula/orbitofrontal cortex responded during revision of a prepared route. Partial specialisations likely arise from distinct connectivity, while widespread copying of task representations reflects strong information exchange. Classical approaches to control, I suggest, should be discarded in favour of a whole-brain approach to construction and use of mental models.