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Decision making is a core competence for animals and humans acting and surviving in environments they only partially comprehend, gaining rewards and punishments for their troubles. Decision-theoretic concepts permeate experiments and computational models in ethology, psychology, and neuroscience. Here, we review a well-known, coherent Bayesian approach to decision making, showing how it unifies issues in Markovian decision problems, signal detection psychophysics, sequential sampling, and optimal exploration and discuss paradigmatic psychological and neural examples of each problem. We discuss computational issues concerning what subjects know about their task and how ambitious they are in seeking optimal solutions; we address algorithmic topics concerning model-based and model-free methods for making choices; and we highlight key aspects of the neural implementation of …