An important component of the risks from climate change arises from outcomes that are very unlikely, but whose impacts if they were to occur would be extremely severe. Examples include levels of surface warming, or changes in the water cycle, that are at the extreme of plausible ranges, or crossing of a climate system “tipping point” such as ice sheet or ocean circulation instability. If such changes were to occur their impacts on infrastructure or ecosystems may exceed existing plans for adaptation. The traditional approach of ensemble climate change projections is not well suited to managing these High Impact-Low Likelihood (HILL) risks, where the objective is to “prepare for the worst” rather than to “plan for what's likely.” In this paper we draw together a number of ideas from recent literature, to classify four types of HILL climate outcome and to propose the development of a practical “toolkit” of physical climate information that can be used in future to inform HILL risk management. The toolkit consists of several elements that would need to be developed for each plausible HILL climate outcome, then deployed individually to develop targeted HILL risk management approaches for individual sectors. We argue that development of the HILL toolkit should be an important focus for physical climate research over the coming decade, and that the time is right for a focused assessment of HILL risks by the Intergovernmental Panel on Climate Change in its 7th Assessment Cycle.