**Winner of the 2019 Sussex International Theory Prize** Despite the science and the summits, leading capitalist states have not achieved anything close to an adequate level of carbon mitigation. There is now simply no way to prevent the planet breaching the threshold of two degrees Celsius set by the Intergovernmental Panel on Climate Change. What are the likely political and economic outcomes of this? Where is the overheating world heading? To further the struggle for climate justice, we need to have some idea how the existing global order is likely to adjust to a rapidly changing environment. Climate Leviathan provides a radical way of thinking about the intensifying challenges to the global order. Drawing on a wide range of political thought, Joel Wainwright and Geoff Mann argue that rapid climate change will transform the world's political economy and the fundamental political arrangements most people take for granted. The result will be a capitalist planetary sovereignty, a terrifying eventuality that makes the construction of viable, radical alternatives truly imperative.