Central ideas from thermal biology, including thermal performance curves and tolerances, have been widely used to evaluate how changes in environmental means and variances generate changes in fitness, selection and microevolution in response to climate change. We summarize the opportunities and challenges for extending this approach to understanding the consequences of extreme climatic events. Using statistical tools from extreme value theory, we show how distributions of thermal extremes vary with latitude, time scale and climate change. Second, we review how performance curves and tolerances have been used to predict the fitness and evolutionary responses to climate change and climate gradients. Performance curves and tolerances change with prior thermal history and with time scale, complicating their use for predicting responses to thermal extremes. Third, we describe several recent case studies showing how infrequent extreme events can have outsized effects on the evolution of performance curves and heat tolerance. A key issue is whether thermal extremes affect reproduction or survival, and how these combine to determine overall fitness. We argue that a greater focus on tails—in the distribution of environmental extremes, and in the upper ends of performance curves—is needed to understand the consequences of extreme events.