The statistics of extremes have played an important role in engineering practice for water resources design and management. How recent developments in the statistical theory of extreme values can be applied to improve the rigor of hydrologic applications and to make such analyses more physically meaningful is the central theme of this paper. Such methodological developments primarily relate to maximum likelihood estimation in the presence of covariates, in combination with either the block maxima or peaks over threshold approaches. Topics that are treated include trends in hydrologic extremes, with the anticipated intensification of the hydrologic cycle as part of global climate change. In an attempt to link downscaling (i.e., relating large-scale atmosphereocean circulation to smaller-scale hydrologic variables) with the statistics of extremes, statistical downscaling of hydrologic extremes is considered. Future challenges are reviewed, such as the development of more rigorous statistical methodology for regional analysis of extremes, as well as the extension of Bayesian methods to more fully quantify uncertainty in extremal estimation. Examples include precipitation and streamflow extremes, as well as economic damage associated with such extreme events, with consideration of trends and dependence on patterns in atmosphere-ocean circulation (e.g., El Niñ no phenomenon).

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