Recent advances in fullerene-based Schottky organic solar cells (OSCs) are presented, with a focus on the current understanding of device physics. Fullerene-based Schottky OSCs attain high open-circuit voltages due to the n-type Schottky junction formed between fullerene and an adjacent high work function anode. Small concentrations of donor material doped into the fullerene matrix serve as efficient exciton dissociation and hole transport agents that can substantially bolster short-circuit currents and fill factors. As a consequence, fullerene-based Schottky OSCs have been demonstrated to provide some of the highest-performance vacuum-deposited small molecule OSCs, with power conversion efficiencies up to 8.1%. Fullerene-based Schottky OSCs constructed using different donor materials and varying cathode buffer layers, as studied by a number of different research groups, are presented. To elucidate the differences between Schottky OSCs and more traditional bulk-heterojunction OSCs, we discuss the photophysics of fullerenes, the role of the donor material, and charge transport in low donor concentration active layers. Fullerene-based Schottky OSCs possess considerable advantages because they can reach high efficiencies with a simple structure using readily available and cost-effective materials. The impact and applicability of the Schottky device architecture on the field of organic photovoltaics at large are discussed.