This paper surveys the measurement of trade costs --- what we know, and what we don't know but may usefully attempt to find out. Partial and incomplete data on direct measures of costs go together with inference on implicit costs from trade flows and prices. Total trade costs in rich countries are large. The ad valorem tax equivalent is about 170% when pushing the data very hard. Poor countries face even higher trade costs. There is a lot of variation across countries and across goods within countries, much of which makes economic sense. Theory looms large in our survey, providing interpretation and perspective on the one hand and suggesting improvements for the future on the other hand. Some new results are presented to apply and interpret gravity theory properly and to handle aggregation appropriately.