The U.S. dollar exchange rate clears the global market for dollar-denominated safe assets. We find that shifts in the demand and supply of safe dollar assets are important drivers of variation in the dollar exchange rate, bond yields, and other global financial variables. An increase in the convenience yield that foreign investors derive from holding safe dollar assets causes the dollar to appreciate, and incentivizes foreign debtors to tilt their issuance towards dollar-denominated instruments. U.S. monetary policy also affects the dollar exchange rate through its impact on the supply of safe dollar assets and the convenience yield. Interest rate spreads with foreign countries are not sufficient statistics to gauge the impact of the stance of U.S. monetary policy on currency markets. The U.S. Treasury basis, which measures the yield on an actual U.S. Treasury minus the yield on an equivalent synthetic U.S. Treasury constructed from a foreign bond, provides a direct measure of the global scarcity of dollar safe assets.