Here we consider how extreme events, particularly climatic and biotic, affect the physiology, development, ecology and evolution of organisms, focusing on plants. The marked effects on organisms are of increasing interest for ecological prediction, given the natural and anthropogenic changes in spectra of extreme events being induced by global change. Yet there is currently a paucity of knowledge or even a common world-view of how extreme events shape individuals, communities and We propose that extreme events need be defined in terms of organisecosystems. mal responses of acclimation and of de-acclimation or hysteresis. From this definition we proceed to develop a number of hypotheses, including that fitness effects of extreme events occur primarily during recovery. We review evidence that, on the evolutionary time scale, selection is, virtually absent except during extreme events; these drive strong directional selection, even to trait fixation and speciation. We describe a number of new tools, both conceptual and technological, that are now at hand or that merit rapid development.