Atmospheric rivers (ARs) are characterized by intense moisture transport, which, on landfall, produce precipitation which can be both beneficial and destructive. ARs in California, for example, are known to have ended drought conditions but also to have caused substantial socio-economic damage from landslides and flooding linked to extreme precipitation. Understanding how AR characteristics will respond to a warming climate is, therefore, vital to the resilience of communities affected by them, such as the western USA, Europe, East Asia and South Africa. In this Review, we use a theoretical framework to synthesize understanding of the dynamic and thermodynamic responses of ARs to anthropogenic warming and connect them to observed and projected changes and impacts revealed by observations and complex models. Evidence suggests that increased atmospheric moisture (governed by Clausius–Clapeyron scaling) will enhance the intensity of AR-related precipitation — and related hydrological extremes — but with changes that are ultimately linked to topographic barriers. However, due to their dependency on both weather and climate-scale processes, which themselves are often poorly constrained, projections are uncertain. To build confidence and improve resilience, future work must focus efforts on characterizing the multiscale development of ARs and in obtaining observations from understudied regions, including the West Pacific, South Pacific and South Atlantic.