The power conversion efficiencies (PCEs) of organic solar cells (OSCs) have improved considerably in recent years with the development of fused-ring electron acceptors (FREAs). Currently, FREAs-based OSCs have achieved high PCEs of over 19% in single-junction OSCs. Whereas the relatively high synthetic complexity and the low yield of FREAs typically result in high production costs, hindering the commercial application of OSCs. In contrast, noncovalently fused-ring electron acceptors (NFREAs) can compensate for the shortcomings of FREAs and facilitate large-scale industrial production by virtue of the simple structure, facile synthesis, high yield, low cost, and reasonable efficiency. At present, OSCs based on NFREAs have exceeded the PCEs of 15% and are expected to reach comparable efficiency as FREAs-based OSCs. Here, recent advances in NFREAs in this review provide insight into improving the performance of OSCs. In particular, this paper focuses on the effect of the chemical structures of NFREAs on the molecule conformation, aggregation, and packing mode. Various molecular design strategies, such as core, side-chain, and terminal group engineering, are presented. In addition, some novel polymer acceptors based on NFREAs for all-polymer OSCs are also introduced. In the end, the paper provides an outlook on developing efficient, stable, and low-cost NFREAs for achieving commercial applications.