An organism's survival depends on its ability to learn about its environment and to make adaptive decisions in the service of achieving the best possible outcomes in that environment. To study the neural circuits that support these functions, researchers have increasingly relied on models that formalize the computations required to carry them out. Here, we review the recent history of computational modeling of learning and decision-making, and how these models have been used to advance understanding of prefrontal cortex function. We discuss how such models have advanced from their origins in basic algorithms of updating and action selection to increasingly account for complexities in the cognitive processes required for learning and decision-making, and the representations over which they operate. We further discuss how a deeper understanding of the real-world complexities in these computations has shed light on the fundamental constraints on optimal behavior, and on the complex interactions between corticostriatal pathways to determine such behavior. The continuing and rapid development of these models holds great promise for understanding the mechanisms by which animals adapt to their environments, and what leads to maladaptive forms of learning and decision-making within clinical populations.