Mg-based materials have been intensively studied for hydrogen storage applications due to their high energy density up to 2600 Wh/kg or 3700 Wh/L. However, the Mg-based materials with poor kinetics and the necessity for a high temperature to achieve 0.1 MPa hydrogen equilibrium pressure limit the applications in the onboard storage in Fuel cell vehicles (FCVs). Over the past decades, many methods have been applied to improve the hydriding/dehydriding (H/D) kinetics of Mg/MgH by forming amorphous or nanosized particles, adding catalysts and employing external energy field, etc. However, which method is more effective and the intrinsic mechanism they work are widely differing versions. The hydrogenation and dehydrogenation behaviors of Mg-based alloys analyzing by kinetic models is an efficient way to reveal the H/D kinetic mechanism. However, some recently proposed models with physical meaning and simple analysis method are not known intimately by researchers. Therefore, this review focuses on the enhancement method of kinetics in Mg-based hydrogen storage materials and introduces the new kinetic models.