This chapter reviews theories proposing that the brain implements statistically optimal strategies for decision-making on the basis of noisy information. These strategies maximize the accuracy and speed of decisions, as well as the rate of receiving rewards for correct choices. The chapter reviews computational models of cortical decision circuits that can optimally perform choices between two alternatives. It has been proposed that the optimal strategy for choice between multiple alternatives is implemented in the cortico-basal-ganglia circuit. A model of cortico-basal-ganglia circuit that implements the optimal strategy for choice between multiple alternatives has been described. In the proposed model, the cortico-basal-ganglia circuit computes the posterior probabilities of alternatives being correct, given the sensory evidence. Furthermore, the chapter shows how the basal ganglia may modulate decision processes in the cortex, allowing cortical neurons to represent the probabilities of alternative choices being correct. For each set of theories, their predictions are compared with existing experimental data.