Exporting is harder than selling at home, and overcoming barriers takes time. We identify key obstacles to exporting and measure their importance by developing a model of firm-level export dynamics with costly customer search, visibility effects, and learning about product appeal. Fitting the model to U.S. import data on Colombian manufactures, we replicate patterns of exporter maturation. A firm’s customer base and market knowledge are valuable intangible assets: losing both through “market amnesia” would cost Colombian exporters US$14.2 billion, over twice annual exports to the U.S. About a quarter of this reflects lost future sales to current customers; the rest stems from the cost of relearning product appeal and regaining visibility. The frictions we estimate slow trade’s response to shocks: the 10-year export sales response to an exchange rate shock is 48 percent larger than the 1-year response.