In today's clinics, a cellular-resolution view of the cornea can be achieved only with an in vivo confocal microscope (IVCM) in contact with the eye. Here, we present a common-path Full-field/Spectral-domain OCT microscope (FF/SD OCT), which, for the first time, enables cell-detail imaging of the entire ocular surface (central and peripheral cornea, limbus, sclera, tear film) without contact and in real time. The device, that has been successfully tested in human subjects, is now ready for direct implementation in clinical research. Real-time performance is achieved through rapid axial eye tracking and simultaneous defocusing correction. Images, extracted from realtime videos, contain cells and nerves, which can be quantified over a millimetric field-of-view, beyond the capability of IVCM and conventional OCT. In the limbus, Palisades of Vogt, vessels and blood flow can be resolved with high contrast without contrast agent injection. The fast imaging speed of 275 frames/s (0.6 billion pixels/s) allowed direct monitoring of blood flow dynamics, enabling creation of high-resolution velocity maps for the first time. Tear flow velocity and evaporation time could be measured without fluorescein administration. 1440 pixels, is captured by a 2D CMOS camera in 3.5 ms at 275 FFOCT frames/s (or 0.6 billion pixels/s), which is 130 times faster (in terms of pixel rate) than the state-of-the-art corneal confocal scanning systems, imaging at 30