The quantitative study of decision-making has traditionally rested on three key behavioral measures: accuracy, response time, and confidence. Of these, confidence—defined as the degree of belief, prior to feedback, that a decision is correct—is least well understood at the level of neural mechanism, although recent years have seen a surge in interest in the topic among theoretical and systems neuroscientists. Here we review some of these developments and highlight a particular candidate mechanism for assigning confidence in a perceptual decision. The mechanism is appealing because it is rooted in the same decision-making framework—bounded accumulation of evidence—that successfully explains accuracy and reaction time in many tasks, and it is validated by neurophysiology and microstimulation experiments.