In the present scenario, much importance has been provided to hydrogen energy systems (HES) in the energy sector because of their clean and green behavior during utilization. The developments of novel techniques and materials have focused on overcoming the practical difficulties in the HES (production, storage and utilization). Comparatively, considerable attention needs to be provided in the hydrogen storage systems (HSS) because of physical-based storage (compressed gas, cold/cryo compressed and liquid) issues such as low gravimetric/volumetric density, storage conditions/parameters and safety. In material-based HSS, a high amount of hydrogen can be effectively stored in materials via physical or chemical bonds. In different hydride materials, Mg-based hydrides (Mg–H) showed considerable benefits such as low density, hydrogen uptake and reversibility. However, the inferior sorption kinetics and severe oxidation/contamination at exposure to air limit its benefits. There are numerous kinds of efforts, like the inclusion of catalysts that have been made for Mg–H to alter the thermodynamic-related issues. Still, those efforts do not overcome the oxidation/contamination-related issues. The developments of Mg–H encapsulated by gas-selective polymers can effectively and positively influence hydrogen sorption kinetics and prevent the Mg–H from contaminating (air and moisture). In this review, the impact of different polymers (carboxymethyl cellulose, polystyrene, polyimide, polypyrrole, polyvinylpyrrolidone, polyvinylidene fluoride, polymethylpentene, and poly(methyl methacrylate)) with Mg–H systems has been systematically reviewed. In polymer-encapsulated Mg–H, the polymers act as a barrier for the reaction between Mg–H and O2/H2O, selectively allowing the H2 gas and preventing the aggregation of hydride nanoparticles. Thus, the H2 uptake amount and sorption kinetics improved considerably in Mg–H.