The power conversion efficiency of the most efficient organic photovoltaic (OPV) cells has recently increased to over 10%. To enable further increases, the factors limiting the device efficiency in OPV must be identified. In this review, the operational mechanism of OPV cells is explained and the detailed balance limit to photovoltaic energy conversion, as developed by Shockley and Queisser, is outlined. The various approaches that have been developed to estimate the maximum practically achievable efficiency in OPV are then discussed, based on empirical knowledge of organic semiconductor materials. Subsequently, approaches made to adapt the detailed balance theory to incorporate some of the fundamentally different processes in organic solar cells that originate from using a combination of two complementary, donor and acceptor, organic semiconductors using thermodynamic and kinetic approaches are described. The more empirical formulations to the efficiency limits provide estimates of 1012%, but the more fundamental descriptions suggest limits of 2024% to be reachable in single junctions, similar to the highest efficiencies obtained for crystalline silicon p-n junction solar cells. Closing this gap sets the stage for future materials research and development of OPV.