There is growing interest in identifying the impacts of extreme climate events on natural systems. Two principles of such detection are that it should be based on a scientific understanding of the processes by which climate affects the system of interest and that non-climate factors that also affect the system should be controlled for. Using a simple temperature-dependent predator-prey model, this paper illustrates the importance of these principles in the context of establishing a link between temperature and population extremes. The results suggest that a naive approach based only on the co-occurrence of temperature and population extremes may fail. In the second part of the paper, some reasons for focusing attention on the ecological impacts of extreme climate events are briefly reviewed. It is suggested that, while extreme ecological events may be important for society, this does not imply that an analysis aimed at connecting them to extreme climate events should necessarily be based on extreme events themselves.This article is part of the themed issue 'Behavioural, ecological and evolutionary responses to extreme climatic events'.