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We report light-driven levitation of macroscopic polymer films with nanostructured surface as candidates for long-duration near-space flight. We levitated centimeter-scale disks made of commercial 0.5-micron-thick mylar film coated with carbon nanotubes on one side. When illuminated with light intensity comparable to natural sunlight, the polymer disk heats up and interacts with incident gas molecules differently on the top and bottom sides, producing a net recoil force. We observed the levitation of 6-mm-diameter disks in a vacuum chamber at pressures between 10 and 30 Pa. Moreover, we controlled the flight of the disks using a shaped light field that optically trapped the levitating disks. Our experimentally validated theoretical model predicts that the lift forces can be many times the weight of the films, allowing payloads of up to 10 milligrams for sunlight-powered low-cost microflyers at altitudes of 50 to 100 km.