We study the gains from trade in a new model with oligopolistic competition, firm heterogeneity, and innovation. Lowering trade costs reduces markups on domestic sales but increases markups on export sales, as firms do not pass the entire reduction in trade costs onto foreign consumers. Trade liberalisation can also reduce the number of firms competing in each market, thereby increasing markups on both domestic and export sales. For the majority of exporters, however, the procompetitive effect prevails and their avera ge markups decline. The incomplete pass-though and the reduction in the number of competitors instead dominate for top-exporters – the top 0:1% of firms which end up increasing their markup. In a quantitative exercise we find that the aggregate effect of trade-induced markup changes is pro-competitive and accounts for the majority of the welfare gains from trade. Trade-induced changes in competition affect survival on domestic and export markets and firms’ decision to innovate. All exporters, and especially the top exporters, increase their market size after liberalisation which, in turn, encourages them to innovate more. Hence, top exporters contribute negatively to welfare gains by increasing their markups but positively by increasing innovation and productivity. Firms’ innovation response accounts for a small but non-negligible share of the welfare gains while the contribution of selection is U-shaped, being negative for small liberalisations and positive otherwise. A more globalised economy is therefore populated by larger, fewer and more innovative firms, each feature representing an important source of the gains from trade.