Nuclear war is clearly a global catastrophic risk, but it is not an existential risk as is sometimes carelessly claimed. Unfortunately, the consequence and likelihood components of the risk of nuclear war are both highly uncertain. In particular, for nuclear wars that include targeting of multiple cities, nuclear winter may result in more fatalities across the globe than the better-understood effects of blast, prompt radiation, and fallout. Electromagnetic pulse effects, which could range from minor electrical disturbances to the complete collapse of the electric grid, are similarly highly uncertain. Nuclear war likelihood assessments are largely based on intuition, and they span the spectrum from zero to certainty. Notwithstanding these profound uncertainties, we must manage the risk of nuclear war with the knowledge we have. Benefit-cost analysis and other structured analytic methods applied to evaluate risk mitigation measures must acknowledge that we often do not even know whether many proposed approaches (e.g., reducing nuclear arsenals) will have a net positive or negative effect. Multidisciplinary studies are needed to better understand the consequences and likelihood of nuclear war and the complex relationship between these two components of risk, and to predict both the direction and magnitude of risk mitigation approaches.