The impactful nature of extreme weather events calls for a robust quantification of their statistics, if risks are to be reliably characterized for both current and future hazards. In this chapter, using examples from recent events, we describe the rationale and some applications of the main statistical tools for such quantification, Extreme Value Analysis, EVA. We present the basic modeling of block maxima through Generalized Extreme Value distributions and that of threshold exceedances, through the Generalized Pareto distribution, and point at some effective extensions of the standard models that enable accounting for time-varying behavior and the joint modeling of phenomena over spatial domains. A section of this chapter is devoted to the description of how to characterize the uncertainty around the central estimates of various extreme metrics of interest, using both empirical (e.g., bootstrap) and formula-based approaches. The chapter concludes with a section that describes a particularly timely application of extreme event modeling: Extreme event attribution, by which the role of anthropogenic climate change in the behavior of a given class of observed events—usually having had large impacts—is quantified.