We review recent progress in the development of organic bulk heterojunction (BHJ) solar cells employing donor–acceptor copolymers as the electron-donor and fullerene derivatives as the electron-acceptor. We discuss the role of the donor and acceptor moieties, side-chains, bridging units and atomic substitutions of the copolymers on their optoelectronic functionality. The physical properties, e.g. molecular conformation, miscibility, phase-separated lateral and vertical morphology, of various photovoltaic blends prepared via solution casting and post-treatments are reviewed and correlated with photovoltaic device performance. Factors influencing the morphological stability of polymer:fullerene BHJ thin-films are briefly discussed. Finally, we address the use of thin organic interlayers to increase the efficiency of BHJ solar cells.