When different climatic extremes occur simultaneously or in close succession, the impacts to the environment, built infrastructure, and society at large are often significantly escalated. These events are collectively referred to as “compound” events. Although they are typically regarded as highly “surprising” when they occur, the dependencies and multi-scale nature of many climate phenomena mean that such events occur much more likely than might be expected by random chance alone. However, despite their high impacts, compound extremes are not, or only poorly covered in current risk analysis frameworks and policy agendas. Floods in particular, are rarely a function of just one driver. Rather, they often arise through the joint occurrence of different source mechanisms. This can include oceanographic drivers such as tides, storm surges, or waves, as well as hydrologic drivers such as rainfall runoff (pluvial) or river discharge (fluvial). Often, two or more of these flood drivers affect the same region and are correlated with each other. For the U.S. coast, it has been shown that dependencies between extreme precipitation and extreme sea levels have changed in many locations, imposing a new type of non-stationarity which has not been accounted for in risk assessments. Such events are classified as “multivariate”. Spatial correlations, even when focusing only on one flooding driver (such as storm surges), are also often ignored in risk assessments, where at-site extreme value distributions are used as input; such events are classified as “spatially compounding”. This presentation will briefly introduce the different types of compound flooding and provide an overview of existing statistical modelling tools to identify and simulate relevant dependencies of flooding drivers. Some of the most pressing challenges in developing improved strategies to assess and mitigate the risks of compound extremes will be discussed, which also includes addressing connections between purely physical (through the climate system) and societal drivers.