Deep trade agreements are widespread and have taken the world beyond tariff liberalization in goods trade. As the importance of global supply chains and the services sector increased across the world, shallow tariff reductions gave way to deeper commitments that address non-tariff barriers and behind the border barriers to trade. This paper shows that deep trade agreement commitments increase trade by 25% for trade in goods and by even more for trade in services. Taking reducedform estimates to a quantitative model enables general equilibrium analysis of the trade and welfare impacts of deep trade agreements. We find that China, India, and the Eastern European bloc have benefited the most from trade agreements since the Uruguay Round. While a large share of the gains to Eastern Europe come from deep commitments during its accession to the EU, gains for China and India come largely from tariff reductions. Applying the framework to ex-ante analysis of the UK's departure from the deepest trade agreement in the world suggests that the potential benefits the UK may gain, post-Brexit, from future deep agreements with the EU and selected non-EU trade partners would not offset its losses from leaving the EU. Overall, deep trade agreements have contributed over 40% to the welfare gains from trade globally and even more so for advanced economies.