A large number of recent studies have aimed at understanding short-duration rainfall extremes, due to their impacts on flash floods, landslides and debris flows and potential for these to worsen with global warming. This has been led in a concerted international effort by the INTENSE Crosscutting Project of the GEWEX (Global Energy and Water Exchanges) Hydroclimatology Panel. Here, we summarize the main findings so far and suggest future directions for research, including: the benefits of convection-permitting climate modelling; towards understanding mechanisms of change; the usefulness of temperature-scaling relations; towards detecting and attributing extreme rainfall change; and the need for international coordination and collaboration. Evidence suggests that the intensity of long-duration (1 day+) heavy precipitation increases with climate warming close to the Clausius–Clapeyron (CC) rate (6–7% K−1), although large-scale circulation changes affect this response regionally. However, rare events can scale at higher rates, and localized heavy short-duration (hourly and sub-hourly) intensities can respond more strongly (e.g. 2 × CC instead of CC). Day-to-day scaling of short-duration intensities supports a higher scaling, with mechanisms proposed for this related to local-scale dynamics of convective storms, but its relevance to climate change is not clear. Uncertainty in changes to precipitation extremes remains and is influenced by many factors, including large-scale circulation, convective storm dynamics andstratification. Despite this, recent research has increased confidence in both the detectability and understanding of changes in various aspects of intense short-duration rainfall. To make further progress, the international coordination of datasets, model experiments and evaluations will be required, with consistent and standardized comparison methods and metrics, and recommendations are made for these frameworks.