The active layer in a solution processed organic photovoltaic device comprises a light absorbing electron donor semiconductor, typically a polymer, and an electron accepting fullerene acceptor. Although there has been huge effort targeted to optimize the absorbing, energetic, and transport properties of the donor material, fullerenes remain as the exclusive electron acceptor in all high performance devices. Very recently, some new non-fullerene acceptors have been demonstrated to outperform fullerenes in comparative devices. This Account describes this progress, discussing molecular design considerations and the structure-property relationships that are emerging. The motivation to replace fullerene acceptors stems from their synthetic inflexibility, leading to constraints in manipulating frontier energy levels, as well as poor absorption in the solar spectrum range, and an inherent tendency to undergo postfabrication crystallization, resulting in device instability. New acceptors have to address these limitations, providing tunable absorption with high extinction coefficients, thus contributing to device photocurrent. The ability to vary and optimize the lowest unoccupied molecular orbital (LUMO) energy level for a specific donor polymer is also an important requirement, ensuring minimal energy loss on electron transfer and as high an internal voltage as possible. Initially perylene diimide acceptors were evaluated as promising acceptor materials. These electron deficient aromatic molecules can exhibit good electron transport, facilitated by close packed herringbone crystal motifs, and their energy levels can be synthetically tuned. The principal drawback of this class of materials, their tendency to crystallize on too large a length scale for an optimal heterojunction nanostructure, has been shown to be overcome through introduction of conformation twisting through steric effects. This has been primarily achieved by coupling two units together, forming dimers with a large intramolecular twist, which suppresses both nucleation and crystal growth. The generic design concept of rotationally symmetrical aromatic small molecules with extended π orbital delocalization, including polyaromatic hydrocarbons, phthalocyanines, etc., has also provided some excellent small molecule acceptors. In most cases, additional electron withdrawing functionality, such as imide or ester groups, can be incorporated to stabilize the LUMO and improve properties. New calamitic acceptors have been developed, where molecular orbital hybridization of electron rich and poor segments can be judiciously employed to precisely control energy levels. Conformation and intermolecular associations can be controlled by peripheral functionalization leading to optimization of crystallization length scales. In particular, the use of rhodanine end groups, coupled electronically through short bridged aromatic chains, has been a successful strategy, with promising device efficiencies attributed to high lying LUMO energy levels and subsequently large open circuit voltages.