Fisher-Tippett-Gnedenko theorem: block maxima converge to GEV(μ,σ,ξ). The shape ξ determines the tail: ξ→0 gives Gumbel (light tail, e.g. Gaussian maxima), ξ>0 Fréchet (heavy tail, power law), ξ<0 Weibull (bounded tail). Return levels for rare events.