Policy-making is usually about risk management. Thus, the handling of uncertainty in science is central to its support of sound policy-making. There is value in scientists engaging in a deep conversation with policy-makers and others, not merely ‘delivering’ results or analyses and then playing no further role. Communicating the policy relevance of different varieties of uncertainty, including imprecision, ambiguity, intractability and indeterminism, is an important part of this conversation. Uncertainty is handled better when scientists engage with policy-makers. Climate policy aims both to alter future risks (particularly via mitigation) and to take account of and respond to relevant remaining risks (via adaptation) in the complex causal chain that begins and ends with individuals. Policy-making profits from learning how to shift the distribution of risks towards less dangerous impacts, even if the probability of events remains uncertain. Immediate value lies not only in communicating how risks may change with time and how those risks may be changed by action, but also in projecting how our understanding of those risks may improve with time (via science) and how our ability to influence them may advance (via technology and policy design). Guidance on the most urgent places to gather information and realistic estimates of when to expect more informative answers is of immediate value, as are plausible estimates of the risk of delaying action. Risk assessment requires grappling with probability and ambiguity (uncertainty in the Knightian sense) and assessing the ethical, logical, philosophical and economic underpinnings of whether a target of ‘50 per cent chance of remaining under +2 ° C' is either ‘right’ or ‘safe’. How do we better stimulate advances in the difficult analytical and philosophical questions while maintaining foundational scientific work advancing our understanding of the phenomena? And provide immediate help with decisions that must be made now?