Organic solar cells (OSCs) enjoy a huge market and public attention as an emerging renewable and clean energy source due to their accessibility, sustainability, translucency, good flexibility, non-toxicity, and low preparation cost. However, the choice of an acceptor material is now the pivotal factor restricting the development of OSCs. To continuously improve stability and increase power conversion efficiency (PCE) for better performance, high-performance acceptor materials are an important part of enabling OSCs. From fullerenes and their derivatives and non-fullerenes, we sum up the latest research progress on high-performance acceptor materials for OSCs and then introduce the synthesis methods of non-fullerenes. The latest strategies to enhance the performance of organic solar cells and the wide range of applications of non-fullerene acceptors (NFAs) on different OSCs are also discussed. In addition, challenges faced by OSCs in improving their performance and the prospects for future development are revealed, providing new ideas for designing the next generation of high-performance OSCs.