Abstract: The DC capacitor voltage of the half-bridge modular multilevel converter (HB-MMC) is distributed in hundreds of submodules, resulting in complex dynamic interaction. The capacitor voltage balance is the key premise for the stable operation of MMC. A fast, reliable and practical MMC capacitor voltage balancing strategy is always the hotspot of engineering and academic research. In this paper, the research progress in recent years is summarized, the voltage balancing strategies with and without the submodule capacitance voltage sampling are reviewed, and the balancing control strategies under special conditions are induced. Finally, the voltage balancing characteristics of the methods above are compared, the future development trend of the MMC capacitor voltage balancing strategies is discussed, and their application prospect is looked forward to, providing a valuable reference for the safe and stable operation of MMC at different voltage levels.