Across the cognitive and behavioral sciences, a distinction is drawn between how we should choose or behave (according to a normative or rational analysis), and how we actually choose or behave (as observed in experiments, and as described by cognitive or neural mechanism theories). This talk presents models based on an alternative perspective that incorporates cognitive bounds into definitions of optimal decision and control, and that explains behavior as a rational adaptation to these bounds. The models offer novel explanations of phenomena in domains of choice, action, attention and language processing, including information-theoretic effects in eye-movements in reading, and choice phenomena that seem to be clear violations of rational decision theory (preference reversals). The kinds of rational explanations offered, and the structure of the models (grounded in state estimation and control and reinforcement learning), both point to a way of using deep reinforcement learning with potentially profound theoretical implications: deep RL can be used to derive cognitive faculties and aspects of mental architecture. To illustrate this potential, we will consider recent deep RL results in language emergence and optimal reward discovery.