I develop and structurally estimate an equilibrium model of the college market. Students, who are heterogeneous in both abilities and preferences, make college application decisions, subject to uncertainty and application costs. Colleges observe only noisy measures of student ability and set up tuition and admissions policies to compete for more able students. The model incorporates tuition, applications, admissions and enrollment as the joint outcome from a subgame perfect Nash equilibrium. I estimate the structural parameters of the model using the NLSY 97 data, via a three-step estimation procedure to deal with potential multiple equilibria. I use the estimated model to perform three counterfactual experiments. First, I explore the impacts of incomplete information on the market. A perfect measure of student ability would lead to higher enrollee ability across colleges and a $2500 increase in average student welfare. Second, I examine the equilibrium consequences of funding cuts to public colleges. All colleges, public and private, increase their tuition, and the drop in student welfare is three times as large as government savings. Finally, I study the extent to which the government can expand college access by increasing the supply of lower-ranked colleges. At most 2.1% more students could be drawn into colleges.