We develop and estimate a structural model of bargaining in firm-to-firm trade to study the determinants of tariff pass-through. The model features oligopoly and oligopsony power and yields analytical expressions for bilateral markups and pass-through based on two sufficient statistics: the supplier‘s share in the buyer‘s purchases and the buyer‘s share in the supplier‘s output. Using U.S. import data, we find substantial importer bargaining power and steep export supply curves. These primitives imply that cost changes, rather than markup adjustments, dominate pass-through, accounting for the bulk of incomplete pass-through of the 2018 U.S. tariffs and its heterogeneity across buyer-supplier links.