This paper studies the optimal climate policy in a global economy. Emissions impose a dynamic, global, negative externality, raising natural questions about international policy coordination. To understand the issues involved, I first build a simple dynamic multi-country model and study the optimal cooperative climate policy that corrects the global externality. Moreover, I move beyond cooperation and study the optimal climate policy for a large country that faces a passive rest of the world. In this setup, corrective taxation motives are intertwined with interest rate manipulation through capital controls. Incentives for carbon taxation are amplified for net importers and mitigated for net exporters.