Abstract: Risk assessment has a rich history in engineering, but conventional methods generally assume that risks are stable, well-characterized, and governed primarily by chance, without the active involvement of competing interests. They also tend to focus on the control of single target risks, overlooking risk-risk tradeoffs and the role of risk attitudes in evaluating the full desirability of alternative actions. These conventions do not hold for most contemporary risks, in which situations are without precedent, conditions are continually changing, and opposing actors have their own motivations. This is especially the case when considering climate change, management of which requires the involvement of multiple powerful parties operating under conditions of high uncertainty, conflicting objectives, and possibly existential threats. In this talk, I will start by describing decision theory and its role in addressing problems involving risk and uncertainty. I will then walk through a series of climate-related decision-making contexts of increasing complexity to exemplify the well-established strengths of the approach, recent advancements that enhance its applicability to addressing climate change, and remaining limitations that require further research and development. Specific climate risks addressed in this talk include the potential for irreversible catastrophe, likely mischaracterization of future social conditions and preferences, possible misestimation of climate response to greenhouse gas emissions, and foreseeable behavioral consequences of solar geoengineering as a climate management strategy.