Geological H2 storage plays a central role to enable the successful transition to the renewable H2 economy and achieve net-zero emission in the atmosphere. Depleted oil and gas reservoirs are already explored with extensive reservoir and operational data. However, residual hydrocarbons can mix with injected H2 in the reservoirs. Furthermore, low density and high diffusivity of H2 may establish H2 leakage from the reservoirs via fault pathways. Interestingly, H2 can be consumed by microorganisms, which results in pore-network precipitation, plugging, and partial permeability impairment. Therefore, stored H2 may be lost in the formations if the storage scenario is not planned cautiously. While salt caverns are safe and commercially proven geo-rock for H2 storage, they have low-storage capacity compared to depleted gas reservoirs. Moreover, salt structures (e.g., domel, bedded) and microorganisms activities in the salt cavern are limiting factors, which can influence the storage process. Accordingly, we discuss challenges and future perspectives of hydrogen storage in different geological settings. We also highlight geographical limitations with diverse microbial communities and theoretical understanding of abiotic transformation (in terms of rock’s minerals, i.e., mica and calcite) for geological H2 storage. Regarding the fundamental behavior of H2 in the geological settings, it is less soluble in formation water; therefore, it may achieve less solubility trapping compared to CO2 and CH4. Furthermore, H2 gas could attain higher capillary entrance pressures in porous media over CH4 and CO2 due to higher interfacial tension. Additionally, the low viscosity of H2 may facilitate its injection and production but H2 may establish the secondary trapping and viscous fingering. Thus, this review documents a blend of key information for the amendment of subsurface H2 storage at the industrial scale.