Fossil fuel alternatives, such as solar energy, are moving to the forefront in a variety of research fields. Polymer-based organic photovoltaic systems hold the promise for a cost-effective, lightweight solar energy conversion platform, which could benefit from simple solution processing of the active layer. The function of such excitonic solar cells is based on photoinduced electron transfer from a donor to an acceptor. Fullerenes have become the ubiquitous acceptors because of their high electron affinity and ability to transport charge effectively. The most effective solar cells have been made from bicontinuous polymer-fullerene composites, or so-called bulk heterojunctions. The best solar cells currently achieve an efficiency of about 5%, thus significant advances in the fundamental understanding of the complex interplay between the active layer morphology and electronic properties are required if this technology is to find viable application.