Harnessing solar energy with solar cells based on organic materials (in particular polymeric solar cells) is an attractive alternative to silicon-based solar cells due to the advantages of lower weight, flexibility, lower manufacturing costs, easier integration with other products, low environmental impact during manufacturing and operations and short energy payback times. However, even with the latest efficiencies reported up to 17%, the reproducibility of these efficiencies is not up to par, with a significant variation in the efficiencies reported across the literature. Since these devices are based on ultrathin multilayer organic films, interfaces play a major role in their operation and performance. This review gives a concise account of the major interfacial issues that are responsible for influencing the device performance, with emphasis on their physical mechanisms. After an introduction to the basic principles of polymeric solar cells, it briefly discusses charge generation and recombination occurring at the donor-acceptor bulk heterojunction interface. It then discusses interfacial morphology for the active layer and how it affects the performance and stability of these devices. Next, the formation of injection and extraction barriers and their role in the device performance is discussed. Finally, it addresses the most common approaches to change these barriers for improving the solar cell efficiency, including the use of interface dipoles. These issues are interrelated to each other and give a clear and concise understanding of the problem of the underperformance due to interfacial phenomena occurring within the device. This review not only discusses some of the implemented approaches that have been adopted in order to address these problems, but also highlights interfacial issues that are yet to be fully understood in organic solar cells.