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Abstract Extreme droughts, heat waves, fires, hurricanes, floods, and landslides cause the largest losses in the United States, and globally, from natural hazards linked to weather and climate. There is evidence that the frequency of such extremes is increasing, particularly for heat waves, large fires, and intense precipitation, making better understanding of the probability and consequences of these events imperative. Further, these events are not isolated, but rather interact with each other and with other social and biophysical drivers and conditions, to amplify impacts. Less is known about the nature and strength of these interactions. Natural and social science subfields frame extreme events with different definitions and analytical approaches, often neglecting interactions and the subsequent novel extremes that can arise. Here we propose a framework for social‐environmental extremes, defined as extraordinary events that emerge from interactions among biophysical and social systems. We argue that this definition is critical because it constrains the focus to major events that are capturing societal and scientific attention because of their extreme biophysical drivers and/or the extreme social outcomes. We review how different fields approach extremes as interacting phenomena and propose a synthetic framework that allows analytical separation of the multiple drivers and responses that yield extreme events and extreme effects. We conclude with a future research agenda for understanding the extreme events that matter to society. This agenda will help to identify where, when, and why communities may have high exposure and vulnerability to social‐environmental extremes—informing future mitigation and adaptation strategies.