We study dynamic stochastic general equilibrium models in which agents are concerned about model uncertainty regarding climate change. An externality from greenhouse gas emissions damages the economy’s capital stock. We assume that the mapping from climate change to damages is subject to uncertainty, and we use robust control theory techniques to study efficiency and optimal policy. We obtain a sharp analytical solution for the implied environmental externality and characterize dynamic optimal taxation. We study optimal output growth in the presence and in the absence of concerns about uncertainty and find that these concerns can lead to substantially different conclusions. We then introduce and study the implications of technological progress.