This paper contributes to the debate on the magnitude of exchange rate elasticities by providing a set of price and quantity elasticities for 51 advanced and emerging-market economies. Specifically, for each of these countries we report the elasticity of trade prices and trade quantities on both the export and on the import sides, as well as the reaction of the trade balance. To that end, we use a large unified database of highly disaggregated bilateral trade flows, covering 5,000 products and more than 160 trading partners. We present a range of estimates using not only standard regression techniques but also generated regressors that aim to address key omitted variable biases, particularly relating to unobserved marginal costs and competitor prices in the importing market. Our results show that quantity elasticities are significantly below one, pass-through is incomplete and export prices react significantly to exchange rate changes. Despite low quantity elasticities, the trade balance reacts positively to a depreciation in all countries because export and import prices adjust. Overall, our findings suggest that changes in the exchange rate can play an important role in addressing global trade imbalances.