Solar radiation will be the largest single source of electricity in a low-carbon future. To maximise the potential of solar power, new materials will be needed to harvest and convert solar energy alongside existing photovoltaic technologies. Molecular electronic materials, such as conjugated polymers and molecules, can achieve photovoltaic conversion through a process of photon absorption, charge separation and charge collection. The materials are appealing because of the potential to tune their properties through chemical design and their compatability with high-throughput manufacture. They are also interesting model systems for photochemical energy conversion because of their parallels with natural photosynthesis. Through a remarkable series of advances in materials design, the efficiency of photovoltaic energy conversion in molecular materials has risen from 1% to over 20% within two decades, surpassing most predictions. We will explore the relationships between the chemical and physical structure of the molecular materials and the function of solar cells, considering the factors that ultimately limit conversion efficiency in such systems. We investigate the potential of single molecular semiconductors, or homojunctions, to achieve efficient solar energy conversion. Finally we consider design criteria for high performance materials and devices.