Extreme events can be a major driver of evolutionary change over geological and contemporary timescales. Outstanding examples are evolutionary diversification following mass extinctions caused by extreme volcanism or asteroid impact. The evolution of organisms in contemporary time is typically viewed as a gradual and incremental process that results from genetic change, environmental perturbation or both. However, contemporary environments occasionally experience strong perturbations such as heat waves, floods, hurricanes, droughts and pest outbreaks. These extreme events set up strong selection pressures on organisms, and are small-scale analogues of the dramatic changes documented in the fossil record. Because extreme events are rare, almost by definition, they are difficult to study. So far most attention has been given to their ecological rather than to their evolutionary consequences. We review several case studies of contemporary evolution in response to two types of extreme environmental perturbations, episodic (pulse) or prolonged (press). Evolution is most likely to occur when extreme events alter community composition. We encourage investigators to be prepared for evolutionary change in response to rare events during long-term field studies. This article is part of the themed issue ‘Behavioural, ecological and evolutionary responses to extreme climatic events’.