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This paper uses a Global Vector Auto-Regression (GVAR) model in a panel of 21 emerging market and advanced economies to investigate the factors behind the dynamics of global trade flows, with a particular view on the issue of global trade imbalances and on the conditions of their unwinding. The GVAR approach enables us to make two key contributions: first, to model international linkages among a large number of countries, which is a key asset given the diversity of countries and regions involved in global imbalances, and second, to model exports and imports jointly. The latter proves to be very important due to the internationalisation of production and the high import content of exports. The model can be used to gauge the effect on trade flows of various scenarios, such as an output shock in the United States, a shock to the US real effective exchange rate and shocks to foreign (German and Chinese) variables. Results indicate in particular that world exports respond much more to a (normalised) shock to US output than to a real effective depreciation of the dollar. In addition, the model can be used to monitor trade developments, such as the sharp contraction in world trade that took place in the wake of the financial crisis. While the fall in imports seems well accounted for by the model, the fall in exports of several countries remains partly unexplained, suggesting perhaps that specific factors might have been at play during the crisis.