To learn how cognition is implemented in the brain, we must build computational models that can perform cognitive tasks, and test such models with brain and behavioral experiments. Cognitive science has developed computational models of human cognition, decomposing task performance into computational components. However, its algorithms still fall short of human intelligence and are not grounded in neurobiology. Computational neuroscience has investigated how interacting neurons can implement component functions of brain computation. However, it has yet to explain how those components interact to explain human cognition and behavior. Modern technologies enable us to measure and manipulate brain activity in unprecedentedly rich ways in animals and humans. However, experiments will yield theoretical insight only when employed to test brain-computational models. It is time to assemble the pieces of the puzzle of brain computation. Here we review recent work in the intersection of cognitive science, computational neuroscience, and artificial intelligence. Computational models that mimic brain information processing during perceptual, cognitive, and control tasks are beginning to be developed and tested with brain and behavioral data.