This paper surveys a wide body of economic literature on the relationship between exchange rates and trade. Specifically, two main issues are investigated: the impact of exchange rate volatility and of currency misalignments on international trade flows. On average, exchange rate volatility has a negative (even if not large) impact on trade. The extent of this effect depends on a number of factors, including the existence of hedging instruments, the structure of production (e.g. the prevalence of small firms), and the degree of economic integration across countries. The second issue involves exchange rate misalignments, which are predicted to have short-run effects in models with price rigidities. However, the exact impact depends on a number of features, such as the pricing strategy of firms engaging in international trade and the importance of global production networks. Trade effects of currency misalignments are predicted to disappear in the long-run, unless an economy is characterized by other relevant distortions. Empirical results broadly confirm these theoretical predictions.