Most trade is invoiced in very few currencies. Yet, standard models assume prices are set in either the producer’s or destination’s currency. We present instead a ‘dominant currency paradigm’ with three key features: pricing in a dominant currency, pricing complementarities, and imported input use in production. We test this paradigm using both a newly constructed data set of bilateral price and volume indices for more than 2,500 country pairs that covers 91% of world trade, and very granular firm-product-country data for Colombian exports and imports. In strong support of the paradigm we find that: (1) Non-commodities terms of trade are essentially uncorrelated with exchange rates. (2) The dollar exchange rate quantitatively dominates the bilateral exchange rate in price pass-through and trade elasticity regressions, and this effect is increasing in the share of imports invoiced in dollars. (3) U.S. import volumes are significantly less sensitive to bilateral exchange rates, compared to other countries’ imports. (4) A 1% U.S. dollar appreciation against all other currencies predicts a 0.6% decline within a year in the volume of total trade between countries in the rest of the world, controlling for the global business cycle.