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The active layer of organic solar cells (OSCs) is composed of a p-type conjugated polymer as the donor and an n-type organic semiconductor as the acceptor. Since the report of bulk-heterojunction OSCs with soluble C60 derivative PCBM as the acceptor in 1995, fullerene derivatives, including PCBM and the C70 derivative PC71BM, have been the dominant acceptors in OSCs for 20 years. In 2015, the A–D–A structured small molecule acceptor (SMA) was developed, which possesses the advantages of a narrow bandgap, strong absorption in the long wavelength region, and suitable electronic energy levels, in contrast to the fullerene derivative acceptors. A–D–A SMAs boost the power conversion efficiency (PCE) of OSCs to the 10–14% level. Recently, benefiting from the innovation of A–DA′D–A structured SMAs, the PCE of OSCs has rapidly increased from 15% to 19%. In this review, the development history of n-type organic semiconductor acceptor materials is briefly introduced. The molecular structures and the physicochemical and photovoltaic properties of acceptors, including fullerene derivatives and narrow bandgap SMAs, are described. In particular, the effect of regulating the molecular packing and miscibility of SMAs on their photovoltaic performance is discussed. Finally, current challenges and prospects for n-type organic semiconductor acceptors are analyzed and discussed.