Multivariate or compound hydrological-extreme events such as successive floods, large-scale droughts, or consecutive drought-to-flood events challenge water management and can be particularly impactful. Still, the multivariate nature of floods and droughts is often ignored by studying individual characteristics only, which can lead to the under- or overestimation of risk. Studying multivariate extremes is challenging because of variable dependencies and because they are even less abundant in observational records than univariate extremes. In this review, I discuss different types of multivariate hydrological extremes and their dependencies, including regional extremes affecting multiple locations, such as spatially connected flood events; consecutive extremes occurring in close temporal succession, such as successive droughts; extremes characterized by multiple characteristics, such as floods with jointly high peak discharge and flood volume; and transitions between different types of extremes, such as drought-to-flood transitions. I present different strategies to describe and model multivariate extremes and to assess their hazard potential, including descriptors of multivariate extremes, multivariate distributions and return periods, and stochastic and large-ensemble simulation approaches. The strategies discussed enable a multivariate perspective on hydrological extremes, which allows us to derive risk estimates for extreme events described by more than one variable.