We review the theory of rotating stars, first developed 80 years ago. Predictions include a specific relation between shape and angular velocity and between surface location and effective temperature and effective gravity. Seen at arbitrary orientation rapidly rotating stars will display ellipsoidal shapes and possibly quite asymmetric intensity distributions. The flattening due to rotation has recently been detected at PTI and VLTI. With the increasing baselines available in the visible and the implementation of closure phase measurements at the NPOI it is now possible to search for the surface brightness effects of rotation. Roche theory predicts only large scale deviations from the usual centro-symmetric limb-darkened models, ideal when the stellar disks are only coarsely imaged as now. We report here observations of Altair and Vega with the NPOI using baselines that detect fringes beyond the first Airy zero in both objects. Asymmetric, non-classical intensity distributions are detected. Both objects appear to be rotating at a large fraction of their breakup velocity. Vega is nearly pole on, accounting for its low apparent rotational velocity. Altair's inclination is intermediate, allowing high S/N detection of all the predicted features of a Roche spheroid. We describe how these objects will test this fundamental theory and how Vega's role as a standard will need reinterpretation.