Hydroclimatic extremes such as intense rainfall, floods, droughts, heatwaves, and wind or storms have devastating effects each year. One of the key challenges for society is understanding how these extremes are evolving and likely to unfold beyond their historical distributions under the influence of multiple drivers such as changes in climate, land cover, and other human factors. Methods for analysing hydroclimatic extremes have advanced considerably in recent decades. Here we provide a review of the drivers, metrics, and methods for the detection, attribution, management, and projection of nonstationary hydroclimatic extremes. We discuss issues and uncertainty associated with these approaches (e.g. arising from insufficient record length, spurious nonstationarities, or incomplete representation of nonstationary sources in modelling frameworks), examine empirical and simulation-based frameworks for analysis of nonstationary extremes, and identify gaps for future research.