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This paper is the first to systematically study the trade effects of economic integration agreements (EIAs) between the European Union - one of the driving forces behind the recent explosion of EIAs - and third countries. We thoroughly disentangle the ex post effects of these EIAs: 1) we allow for differential timing of effects of EIAs, 2) we look at the effects on total trade flows as well as on the margins, 3) we allow for heterogeneity across EIAs and 4) we estimate the effects of EIAs on trade flows for each EU country individually. We use a panel on aggregate imports and exports for the period of 1988-2013 and control for endogeneity of EIAs and multilateral resistance. We find that EIAs have complex and heterogeneous effects on trade flows between the EU and the rest of the world. EIAs have differential effects on trade, depending on the characteristics of the EIAs and the EU member state. We also find that EIAs have positive effects on EU exports, but less on imports, and that a zero effect on the total trade flows sometimes covers opposing effects on the intensive and extensive margins.