The paper considers how extreme events, particularly climatic and biotic, affect the physiology, development, ecology and evolution of organisms, focusing on plants. It is proposed that extreme events need to be defined in terms of organismal responses of acclimation and of de-acclimation or hysteresis. From this a number of hypotheses are developed, including that fitness effects of extreme events occur primarily during recovery. Evidence is reviewed that selection is virtually absent except during extreme events on the evolutionary time scale. Extreme events drive strong directional selection, even to trait fixation and speciation. A number of new tools are described, both conceptual and technological, that are now at hand or that merit rapid development.