Carbon materials are excellent candidates for photovoltaic solar cells: they are Earth-abundant, possess high optical absorption, and superior thermal and photostability. Here we report on solar cells with active layers made solely of carbon nanomaterials that present the same advantages of conjugated polymer-based solar cells - namely solution processable, potentially flexible, and chemically tunable - but with significantly increased photostability and the possibility to revert photodegradation. The device active layer composition is optimized using ab-initio density functional theory calculations to predict type-II band alignment and Schottky barrier formation. The best device fabricated is composed of PC70BM fullerene, semiconducting single-walled carbon nanotubes and reduced graphene oxide. It achieves a power conversion efficiency of 1.3% - a record for solar cells based on carbon as the active material - and shows significantly improved lifetime than a polymer-based device. We calculate efficiency limits of up to 13% for the devices fabricated in this work, comparable to those predicted for polymer solar cells. There is great promise for improving carbon-based solar cells considering the novelty of this type of device, the superior photostability, and the availability of a large number of carbon materials with yet untapped potential for photovoltaics. Our results indicate a new strategy for efficient carbon-based, solution-processable, thin film, photostable solar cells.