Extreme weather events of unprecedented intensity in historical records can have major impacts on society and ecosystems. While adaptation plans often consider past trends in extreme weather events, few consider the possibility of exceptional extremes. This oversight leaves society underprepared and ill-equipped to handle ‘surprising’ events. There is a long history of science inquiry into the question of what low likelihood weather events are possible. Here, we present an overview of the methods used to identify exceptional weather events. We discuss tools for scientists, practitioners and policy-makers to ‘see the unseen’ and evaluate unexpected yet plausible disruptive events. We first discuss existing approaches for estimating rare extremes; then give an example for exceptional heat in The Netherlands; and finally outline how this knowledge can be leveraged to strengthen resilience and adaptation efforts.