The modular multilevel converter (MMC) has been widely adopted in high voltage direct current (HVDC) transmission systems due to its significant advantages. MMC-HVDC is developing towards multi-terminal direct current (MTDC) power grid for reliability enhancement. However, there exist a huge amplitude and a steep rise in fault current due to the low impedances of DC lines and MMCs, which threaten the security and reliability of the DC power grids. It is necessary to restrain the DC short circuit current in order to ensure the safe and stable operation of DC power grids. This paper gives a comprehensive review and evaluation of the proposed DC short-circuit current analysis and suppression techniques used in MMC-based MTDC power girds, in terms of MMC modeling, short circuit calculation, and suppression method. In addition, future trends of countermeasures to short circuit current in MMC-based MTDC power grids are also discussed.