Extreme weather and climate events and their impacts can occur in complex combinations, an interaction shaped by physical drivers and societal forces. In these situations, governance, markets and other decision-making structures—together with population exposure and vulnerability—create nonphysical interconnections among events by linking their impacts, to positive or negative effect. Various anthropogenic actions can also directly affect the severity of events, further complicating these feedback loops. Such relationships are rarely characterized or considered in physical-sciences-based research contexts. Here, we present a multidisciplinary argument for the concept of connected extreme events, and we suggest vantage points and approaches for producing climate information useful in guiding decisions about them.