Friedman (1962) suggested that in general, unfettered markets ensure the efficient provision of goods and services. Applying this logic to Education, he recommended that students be provided with vouchers and allowed to purchase schooling services in a free market ((Friedman (1955, 1962)). Hoxby (2002) refines this argument and suggests that more choice will lead to higher school productivity. We discuss the evidence in this area, concluding that the impact of competition has proven to be more mixed and modest than expected. We suggest that this in fact should not be surprising, since economic theory on incentives and incomplete contracts (beginning with many contributions also from the 1950s) leads to a more nuanced expectation. Specifically, an examination of the incentives faced by schools, parents, and students leads to predictions that are broadly consistent with the evidence, and suggests that there is no a priori reason to believe that school choice will dramatically improve test scores. We describe a simple model that illustrates this point and further implies that elements of market design might be necessary to ensure that competition enhances educational performance.