The performance of solar cells based on molecular electronic materials is limited by relatively low open-circuit voltage (Voc) relative to the absorption threshold. These voltage losses must be reduced to achieve competitive power-conversion efficiencies. Voltage losses are assigned to the molecular heterojunction required to dissociate photogenerated excitons and to relatively fast electron–hole recombination. Recent studies using luminescence have helped quantify these losses and understand their molecular origin. Recently, higher voltages and lower losses have been achieved using new molecular acceptors in place of traditional fullerenes, suggesting that optimizing chemical structure could enable improved device performance. This mini-review combines a device-physics perspective with a body of experimental observations to explore the practical and theoretical limits to Voc.