Uncertainty plagues every modeling effort in hydrogelogy and every decision made on the basis of such models. Given this pervasive uncertainty, virtually every practical problem in hydrogeology can be formulated in terms of (ecologic, monetary, health, regulatory, etc.) risk. This review deals with hydrogeologic applications of the recent advances in uncertainty quantification, probabilistic risk assessment (PRA), and decision under uncertainty. The subjects discussed include probabilistic analyses of exposure pathways, PRAs based on fault tree analyses and other systems-based approaches, PDF (probability density functions) methods for propagating parametric uncertainty through a modeling process, computational tools (e.g., random domain decompositions and transition probability based approaches) for quantification of geologic uncertainty, Bayesian algorithms for quantification of model (structural) uncertainty, computational methods for decision-making under uncertainty (stochastic optimization and decision theory). The review is concluded with a brief discussion of ways to communicate results of uncertainty quantification and risk assessment.