This tutorial lecture describes recent advances in our understanding of how simple decisions are implemented in the brain. The study of decision-making opens a window on the neural basis of many other higher cognitive capacities which also use information in a contingent fashion and in a flexible time frame — free from the immediacy of sensory events or the need to control a body in real time. I will attempt to connect the findings from neural recording and microstimulation experiments to the broader computational problem of inference on data streams. The neurobiology inspires us to reformulate many inference/reasoning problems with explicit incorporation of stopping rules and an interplay between time and probability. These insights were anticipated by Alan Turing in his code-breaking work during World War II, and they were developed by Abraham Wald into the field of Sequential Analysis. Besides its mathematical elegance and strategic importance, this computational mechanism may be essential for higher brain function. If so, the principles revealed by the study of decision-making may one day lead to new treatments for neurological disorders affecting our most cherished cognitive abilities.