Organic photovoltaic (OPV) technology could allow the inexpensive production of flexible solar cells via a roll-to-roll printing process. However, the performance of OPV devices relies on the formation of a nanostructured morphology of small but well-defined domains of donor and acceptor materials. Covalent linkage of the donor and acceptor material into a single block copolymer material could provide a bottom-up approach to the formation of ideal morphologies, but fundamental and multidisciplinary research is required to overcome the limitations facing the successful application of this material class to OPV. In this review, the evolution of block copolymers as OPV active layers and the strategies of material design, morphology control, and synthesis are discussed. Donor/acceptor block copolymers designed as single material OPV active layers and studies of model systems which contribute to the understanding of donor/acceptor block copolymers are the focus. Coil–coil and rod–coil block copolymer systems are examined to inform the discussion on rod–rod type materials, while the synthesis and application of fully-conjugated block copolymers is emphasized as the foremost material design.