Signal Detection Theory (SDT) quantifies decision-making under uncertainty by separating perceptual sensitivity (d′) from response bias indexed by the decision criterion (c). The first section situates SDT historically and frames three guiding themes: bias-free sensitivity, task-general model adaptation, and explicit decision strategies. The next section traces the theory’s conceptual development and contrasts detection with discrimination tasks. The third section formalizes equal- and unequal-variance Gaussian models, derives likelihood-ratio decision rules, and presents receiver-operating-characteristic analysis with continuity corrections for extreme data. The fourth section surveys applications in neuroscience, medicine, consumer science, law, and economics. The fifth section details yes-no, forced-choice, same-different, and rating paradigms and provides software resources for parameter estimation and visualization. The last section offers three case studies—auditory detection and diagnostic radiology—that demonstrate how SDT quantifies sensitivity, locates criteria, and clarifies hit-false-alarm trade-offs. SDT thus remains a versatile analytic framework unifying psychological, neuroscientific, clinical, and economic investigations of perceptual decision-making.