Hydroclimatic extremes such as floods, droughts, storms, or heatwaves often affect large regions and can cluster in time, therefore causing large socio-economic damages. Hazard and risk assessments, aiming at reducing the negative consequences of such extreme events, are often performed with a focus on one location despite the spatially compounding nature of extreme events. Also, clustering of extremes in time is often neglected, with potentially severe underestimation of hazard. While spatial-temporal extremes receive a lot of attention by the media, it remains scientifically and technically challenging to assess their risk by modelling approaches. Key challenges in advancing our understanding of spatio-temporal extremes and in developing new modeling approaches include: the definition of multivariate events; the dealing with large dimensions; the quantification of spatial and temporal dependence, together with the introduction of flexible dependence structures; the identification of potential drivers for spatio-temporal dependence; the estimation of occurrence probabilities, and the linking of different spatial and temporal scales. This session invites contributions which help to better understand processes governing spatio-temporal extremes and/or propose new ways of describing and modeling compounding events at different scales.