In this paper we investigate the importance of fuel costs in shaping world trade. We use AIS data on ship locations and transaction-level shipping prices, along with a dynamic model describing the world shipping industry, to measure the elasticity of trade with respect to ship fuel costs. We find that the average estimated elasticity is 0.35, but ranges from 0.1 to about 1.2 depending on the level of the fuel cost. The pass-through of fuel costs to transport costs is low, at 0.17. Strikingly, the trade elasticity features a pronounced asymmetry in low vs. high oil prices. As fuel costs decline, the elasticity plateaus and further declines have little impact on trade. This "flattening out" of the elasticity is attributed to the equilibrium of the transportation sector and in particular the changes in the relative bargaining positions of ships and exporters. Finally, we use the estimated elasticity to assess the importance of ship design on trade flows: if the large fuel efficiency gains achieved in the 1980s had not been realized, trade would be 12% lower today.