Organic and hybrid organic–inorganic photovoltaics are among the most promising options for low-cost and highly scalable renewable energy. In order to fully realize the potential of these technologies, power conversion efficiencies and stability will both have to be improved beyond the current state-of-the-art. The morphology of the active layer is of paramount importance in the photon to electron conversion process in organic and hybrid solar cells, with all length scales, from molecular ordering to intradevice composition variability, playing key roles. Given the central influence of morphology, characterizing the structure of these surprisingly complex material systems at multiple length scales is one of the grand challenges in the field. This review addresses the techniques, some of which have only recently been applied to organic and hybrid photovoltaics, available to scientists and engineers working to understand—and ultimately improve—the operation of these fascinating devices.