We establish interior estimates for Lp-norms, Orlicz norms, and mean oscillation of second derivatives of solutions to the Monge-Ampère equation detD2u = f(x) with zero boundary value, where f(x) is strictly positive, bounded, and satisfies a VMO-type condition. These estimates develop the regularity theory of the Monge-Ampère equation in VMO-type spaces. Our Orlicz estimates also sharpen Caffarelli's celebrated W2,p-estimates. © 2008 Wiley Periodicals, Inc.