The occurrence of U-shaped dose-response relationships (often termed hormesis) has been documented in numerous biological, toxicological, and pharmacological investigations. Many of the endpoints studied are of considerable significance to public health (e.g. body weight, cholesterol levels, ethanol consumption, longevity, cancer incidence, etc). Despite the fact that U-shaped dose-responses are widely and independently observed, little attempt has been made to assess this phenomenon in an integrative manner. This review provides an overview of the historical foundations of hormesis and a discussion of its definition within a mechanistic framework. The occurrence, generalizability, and biological significance of U-shaped dose-response relationships along with the concept of biological optimality are addressed.