Recently, polymer solar cells developed very fast due to the application of non-fullerence acceptors. Substituting asymmetric small molecules for symmetric small molecule acceptors in the photoactive layer is a strategy to improve the performance of polymer solar cells. The asymmetric design of the molecule is very beneficial for exciton dissociation and charge transport and will also fine-tune the molecular energy level to adjust the open-circuit voltage (V_oc) further. The influence on the absorption range and absorption intensity will cause the short-circuit current density (J_sc) to change, resulting in higher device performance. The effect on molecular aggregation and molecular stacking of asymmetric structures can directly change the microscopic morphology, phase separation size, and the active layer's crystallinity. Very recently, thanks to the ingenious design of active layer materials and the optimization of devices, asymmetric non-fullerene polymer solar cells (A-NF-PSCs) have achieved remarkable development. In this review, we have summarized the latest developments in asymmetric small molecule acceptors (A-NF-SMAs) with the acceptor–donor–acceptor (A–D–A) and/or acceptor–donor–acceptor–donor–acceptor (A–D–A–D–A) structures, and the advantages of asymmetric small molecules are explored from the aspects of charge transport, molecular energy level and active layer accumulation morphology.