In this paper we examine the product space and its consequences for the process of structural transformation. We argue that the assets and capabilities needed to produce one good are imperfect substitutes for those needed to produce other goods, but the degree of asset specificity varies widely. Given this, the speed of structural transformation will depend on the density of the product space near the area where each country has developed its comparative advantage. While this space is traditionally assumed to be smooth and continuous, we find that in fact it is very heterogeneous, with some areas being very dense and others quite sparse. We develop a measure of revealed proximity between products using comparative advantage in order to map this space, and then show that its heterogeneity is not without consequence. The speed at which countries can transform their productive structure and upgrade their exports depends on having a path to nearby goods that are increasingly of higher value. [Jointly published as Center for International Development Working Paper No. 128 and KSG Faculty Research Working Paper Series RWP06-041.]