Meeting the Paris climate goals requires the global economy’s urgent decarbonization. States and intergovernmental bodies insist that this should be pursued via a tremendous spike in private investment in renewable power – encouraged and coordinated by states. However, this renewable investment boom will have to swim against the current of the stagnation of the world economy since the 1970s, characterized by weak rates of investment and growth. Undertaking decarbonization in this context presents unique political economy dilemmas. Firstly, although slow growth helps to reduce carbon emissions by lowering energy use, it simultaneously impedes energy efficiency gains. Secondly, the stagnant state of global industry militates against its adoption of expensive decarbonized industrial processes. Thirdly, while most renewable power sources have failed to attract sufficient investment, those that have expanded rapidly – particularly solar photovoltaic – have tended to exhaust their growth potential due to falling prices and profitability. Finally, economic stagnation has destabilized political institutions, exerting pressures on governments to stimulate growth regardless of the environmental implications. States must navigate these intractable dilemmas as they strategize to decarbonize the downturn.