In this paper, we study trade imbalances between world countries in the period 1960–2011 using a complex-network approach. We show that trade imbalances in absolute value are characterized by a hierarchical arrangement wherein a few developed economies display high clustering and carry an important amount of global-trade imbalances. In contrast, trade imbalances in relative terms show a more fragmented topology, with less concentrated clustering which is particularly high for developing countries. In addition, we find that traditional null random-network models and the gravity model poorly predict the topology of trade imbalance networks. Our main finding is that the evolution of international trade has caused very heterogeneous imbalances in world economies, which may have important consequences for global instability and development.