I define and provide empirical evidence for an "International Price System" in global trade, employing data for thirty-five developed and developing countries. This price system is characterized by two features. First, the overwhelming share of world trade is invoiced in very few currencies, with the dollar the dominant currency. Second, international prices, in their currency of invoicing, are not very sensitive to exchange rates at horizons of up to two years. In this system, a good proxy for a country's inflation sensitivity to exchange rate fluctuations is the fraction of its imports invoiced in a foreign currency. U.S. inflation is consequently more insulated from exchange rate shocks, while other countries are highly sensitive to it. Exchange rate depreciations (appreciations) make U.S. exports cheaper (expensive), while for other countries they mainly raise (lower) mark-ups and hence profits. U.S. monetary policy has spillover effects on inflation in other countries, while spillovers from other countries monetary policies on to U.S. inflation are more muted.