Accelerating global climate change drives new climate risks. People around the world are researching, designing, and implementing strategies to manage these risks. Identifying and implementing sound climate risk management strategies poses nontrivial challenges including (a) linking the required disciplines, (b) identifying relevant values and objectives, (c) identifying and quantifying important uncertainties, (d) resolving interactions between decision levers and the system dynamics, (e) quantifying the trade-offs between diverse values under deep and dynamic uncertainties, (f) communicating to inform decisions, and (g) learning (...) from the decision-making needs to inform research design. Here we review these challenges and avenues to overcome them. ▪ People and institutions are confronted with emerging and dynamic climate risks. ▪ Stakeholder values are central to defining the decision problem. ▪ Mission-oriented basic research helps to improve the design of climate risk management strategies. (shrink)