In case of many decisions based on sensory information, the sensory stimulus or its neural representation are noisy. 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 first reviews computational models of cortical decision circuits that can optimally perform choices between two alternatives. Then, it describes a model of cortico-basal-ganglia circuit that implements the optimal strategy for choice between multiple alternatives. Finally, it 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.