We provide a spatial theory of clean growth to assess the global impact of the rise of renewable energy. We model the details of the combined production and transmission network of electricity (“the grid”) that determine the supply and losses of energy in space. Demand is determined through a model of trade and production, and electricity prices are set by regional grid operators. The local rate of clean energy adoption depends on learning-by-doing, the global electricity and trade network, and regional comparative advantage in renewable resources. To quantify the contribution of renewable adoption to global growth, we collect and harmonize global data on transmission lines, power stations, trade, and regional output. We use the model to measure the aggregate and spatial implications of decarbonizing power production, as well as the role of policy in affecting the transition.