This article traces the development of uncertainty analysis through three generations punctuated by large methodology investments in the nuclear sector. Driven by a very high perceived legitimation burden, these investments aimed at strengthening the scientific basis of uncertainty quantification. The first generation building off the Reactor Safety Study introduced structured expert judgment in uncertainty propagation and distinguished variability and uncertainty. The second generation emerged in modeling the physical processes inside the reactor containment building after breach of the reactor vessel. Operational definitions and expert judgment for uncertainty quantification were elaborated. The third generation developed in modeling the consequences of release of radioactivity and transport through the biosphere. Expert performance assessment, dependence elicitation and probabilistic inversion are among the hallmarks. Third generation methods may be profitably employed in current Integrated Assessment Models (IAMs) of climate change. Possible applications of dependence modeling and probabilistic inversion are sketched. It is unlikely that these methods will be fully adequate for quantitative uncertainty analyses of the impacts of climate change, and a penultimate section looks ahead to fourth generation methods.