The frequency and intensity of extreme precipitation are critical factors for the assessment of future impacts due to rainfall extremes. Other event characteristics can also play an important role: for example, the duration, spatial extent and areal precipitation volume of the event. To fully understand how extreme precipitation may change in a future climate, an analysis encompassing all the properties of extreme precipitation is thus necessary. A two-pronged approach adopting both classical and Lagrangian perspectives on extreme precipitation is thus necessary. In the Lagrangian perspective, precipitation events are viewed as features in space-time to be identified and tracked via a tracking algorithm while assessing their characteristics relative to the transiting storm centre. Intense precipitation events can thus be characterized in terms of their spatial extent, total precipitation volume, mean and maximum intensity, occurrence rate, and – if tracked – also lifetime, distance travelled, speed and area covered. The overarching aim is to investigate and understand potential changes of these feature-based characteristics within a changing climate. For convective precipitation, many of the important underlying processes cannot be directly simulated in standard climate models. As a result, many of the aforementioned characteristics are often poorly represented. Once model resolution is increased to give a grid spacing of less than approximately 4 km, however, convective processes can begin to be directly simulated and the shortcomings of models using parametrized convection are greatly reduced. There is additionally evidence from convection-permitting models (CPMs) that the response to climate change of sub-daily convective extremes may be far stronger than previously thought, and that this intensification can only be demonstrated with CPMs. Our analyses are thus based on climate simulations, both historical and projections, which have been dynamically downscaled by CPMs to convection-permitting resolution, as well as convection-permitting resolution reanalyses.