Growth theory has traditionally assumed the existence of an aggregate production function, whose existence and properties are closely tied to the assumption of optimal resource allocation within each economy. We show extensive evidence, culled from the micro-development literature, demonstrating that the assumption of optimal resource allocation fails radically. The key fact is the enormous heterogeneity of rates of return to the same factor within a single economy, a heterogeneity that dwarfs the cross-country heterogeneity in the economy-wide average return. Prima facie, we argue, this evidence poses problems for old and new growth theories alike. We then review the literature on various causes of this misallocation. We go on to calibrate a simple model which explicitly introduces the possibility of misallocation into an otherwise standard growth model. We show that, in order to match the data, it is enough to have misallocated factors: there also needs to be important fixed costs in production. We conclude by outlining the contour of a possible non-aggregate growth theory, and review the existing attempts to take such a model to the data.