Conventional matrix converters (MCs) have limited voltage gain that is less than 0.866, whether for direct MC (DMC) or indirect MC (IMC). The Z-source MCs (ZSMCs) overcome the voltage gain limitation of the traditionalMC and achieve buck and boost operation with reduced switches count, thereby achieving low cost, high efficiency, and reliability, compared to the back-to-back converter. Furthermore, it will leads to more MC industrial applications. This paper presents an up-to-date comprehensive overview of the different ZSMC topologies and their configurations, circuit analyses, modulation schemes, and applications. This study offers a comprehensive and systematic reference for the future development of the ZSMCs.