Due to the low voltage and high randomness of renewable energy, high-performance grid-connected converters are needed. With the advantages of a high boost ratio, flexible design, and simple control, the Y-Source Converter (YSC) is widely concerned. However, there are a few drawbacks to the traditional Y-source converter, including significant switching stress, voltage voltage overshoot, and discontinuous current. To solve the problems above, a series of improved topologies are proposed. Moreover, the voltage gain, current ripple, and soft switching characteristics have also been optimized. So far, the existing literature lacks the collation and comparison of different topologies of Y-source, as well as the analysis of its evolution process. Therefore, this paper provides a comprehensive overview of Y-source converters’ topologies. According to their features and applications, different topologies are classified and described, leading to guidance for the selection of YSCs under different scenarios. Meanwhile, the working principle, evolution process, and vital issues are analyzed. By revealing their deductive rules, valuable suggestions are provided for the future development of YSCs.