Attention plays many roles in perception and behavior, one of the most basic being the enhancement of responses to subtle stimuli that might otherwise go unnoticed. The computational mechanisms that underlie attention’s role in stimulus detectability can be understood through the framework of signal detection theory (SDT). Attention can improve detectability by modifying signal and noise characteristics, optimizing decision criteria, and pooling across multiple detectors. SDT also provides an integrated account of the effects of stimulus prevalence and the effect of rewards and punishments. Sequential sampling theory extends SDT in the time dimension. By computing detectability metrics across the visual field, one can construct salience maps that take into account stimulus strength, likelihood, and value.