Nowadays, organic solar cells (OSCs) with efficiencies over 10% have been achieved through the elaborate design of electron donors and fullerene acceptors. However, the drawbacks of fullerene acceptors, like poor absorption, limited chemical and energetic tunabilities, high-cost purification and morphological instability, have become the bottlenecks for the further improvement of OSCs. To overcome the mentioned shortages from fullerene, research studies on non-fullerene electron acceptors have boomed. To date, the highest efficiency of fullerene-free OSCs has been pushed to be 12%, which surpasses that of fullerene-based OSCs. In this perspective, we focus on summarizing the development of small molecule electron acceptors designed to replace the fullerene derivatives. Since it has been revealed that the search for matched donor:acceptor pairs is important for accomplishing high efficiencies, we therefore divide electron acceptors into several categories according to the donors used in fullerene-free OSCs. After the introduction of these acceptors, we outline the designing rules as well as perspectives for the development of non-fullerene acceptors. We believe that the development of non-fullerene electron acceptors will make organic photovoltaics closer to practical applications.