We examine how the composition of residential energy consumption and its sensitivity with respect to income changes. The paper characterizes the energy transition, analyzing the behavior of income elasticity of energy demand along the economic development stages by fuel types. The results indicate a nonlinear relationship between income and domestic energy consumption that can be explained by two factors. First, along the income distribution, consumption of modern fuels increases, replacing traditional and transitional fuels until modern fuels drive all of the growth in domestic energy demand. Second, at the highest income levels, income elasticity starts to decrease, leading to concavity in energy consumption. That is, the income elasticity of residential energy demand follows an inverse U-shape along the world income distribution. This finding suggests that at high income levels, residential energy consumption shows satiation and net energy-saving effects.