I investigate the cognitive mechanisms supporting adaptive control over behavior. To be adaptive over both evolutionary timescales and more momentary ones, these cognitive control mechanisms must balance constraints facing many resource-limited systems. I take inspiration from such systems, using formal models to refine hypotheses about how cognitive control may address fundamental constraints. I then test these hypotheses with a convergent cognitive neuroscience approach. I test children and adults using physiological techniques like pupillometry and EEG, and cutting-edge technologies like fMRI and TMS, all building on a computational foundation in neural networks and Bayesian modeling.