Numerous researchers have speculated on and attempted to quantify the impact of policies designed to increase school choice and competition between schools, and they have reached widely differing conclusions. In this article, we provide an overview of the research that focuses on the potential achievement effects of greater private sector competition on K-12 schooling. In particular, we explore the various methodologies that have been used to assess the relative effectiveness of public and private schools. We discuss the strengths and shortcomings of different approaches, and based on this, we ponder what is known and not known about the impact of increased choice and competition. In conclusion, we maintain that although many of the methodologies used to assess the effects of particular interventions, such as educational vouchers, are sound, they likely fail to capture the general equilibrium consequences of enhanced choice. As a result, many of the questions we would want answered to inform policymaking remain unknown.