We build a dynamic trade model to study how international unbundling of production and the emergence of global supply chains affect the world income distribution. We consider a world where countries only differ in their productivity. The level of productivity determines the number of varieties a country produces. To manufacture each variety a bundle of intermediates, which require capital and labor in different proportions, needs to be assembled. We characterize two trade regimes: (i) trade only in varieties and (ii) trade in both varieties and intermediates (unbundling). We show that unbundling of production generates income divergence among ex-ante identical countries (symmetry breaking). With heterogeneous countries, it increases top-bottom inequality and it has non-monotonic effects on the world income distribution (it reduces relatively more the income share of middle-productivity countries). Unbundling of production also increases within-country inequality in all countries. We also show that when the South joins the global supply chain, the income share of all northern and the most productive southern countries increase, at the expense of the least productive countries. In addition, we find that the effect of a labor-saving technology, computerization, depends on the trade regime. Without unbundling, computerization has no effect on the world income distribution. With unbundling, computerization raises world inequality. Finally, we show that technology diffusion leads to income convergence under both trade regimes. However, with unbundling of production more low-productivity countries benefit from technological catch-up.