A unique and very large-scale data collection effort for sub-daily precipitation across multiple continents has produced new insight into the global climatology of sub-daily precipitation extremes from gauge data and their thermodynamic and large-scale drivers. Peak intensities of extreme short-duration rainfall are intensifying more rapidly than would be expected with global warming, with this rapid intensification also borne out by studies on the apparent scaling relation between dew point temperature and extreme hourly precipitation intensities. Alongside this advance has been the development of regional scale radar datasets which have provided new insights on changes to the spatial structure of intense precipitation. Despite this new understanding from observations it is not trivial that these observed relationships will hold in a warming climate. However, the development of new very high resolution convection-permitting model (CPM) simulations that adequately resolve cloud processes at climate-length scales now allow projections to be made for sub-daily precipitation extremes. These have provided insight into mechanisms of change and quantification of changes in extreme precipitation characteristics at up to continental scales and provide clear implications for flash flooding of urban areas and smaller catchments.