Adaptation is a universal process in organisms as diverse as bacteria and humans, and across the various senses. This article proposes a simple, heuristic, mathematical model containing tonic and phasic processes. The model demonstrates properties not commonly associated with adaptation, such as increased sensitivity to changes, range shifting, and phase lead. Changes in only four parameters permit the model to predict empirical psychophysical data from different senses. The relatively prolonged time courses of responses to oral and topical capsaicin are used to illustrate and validate this mathematical modeling approach for different stimulus profiles. Other examples of phenomena elucidated by this modeling approach include the time courses of taste sensation, brightness perception, loudness perception, cross-adaptation to oral irritants, and cutaneous mechanoreception. It also predicts such apparently unrelated phenomena as perceived alcohol intoxication, habituation, and drug tolerance. Because the integration of phasic and tonic components is a conservative, highly efficacious solution to a ubiquitous biological challenge, sensory adaptation is seen as an evolutionary adaptation, and as a prominent feature of Mother Nature's small bag of tricks.