As a clean, efficient energy source, hydrogen is regarded as a promising alternative energy for accomplishing the zero-CO2 targets. In the longer term, large-scale hydrogen geologic storage (HGS) could reduce the instability of intermittent energy sources, through peak cutting and valley filling. However, the low density and viscosity of hydrogen and its interaction with the surrounding rocks and microbes constrain the effective advancement of large-scale HGS. This paper summarizes the current research status, feasibility analysis, advantages and disadvantages of HGS in the main potential reservoirs (depleted oil/gas fields, salt caverns, and brine aquifers). In addition, the uncertainties and challenges are also addressed for HGS application in the future: 1) Operating parameters, which are difficult to determine and evaluate, have a significant impact on HGS efficiency. For example, the cyclical injection-reproduction and injection rates have large impact on H2 fingering phenomenon and the geological integrity of the caprocks; 2) Currently, the hydrogen-water-rock geochemical reactions at various temperatures and pressures are not well understood well. There is a lack of a geochemical reaction database to meet the HGS numerical simulation requirements. The associated reactions could cause uncertain changes in porosity and permeability, which may cause large-scale hydrogen leakage in severe cases; 3) Metabolic mechanisms of subsurface environmental microorganisms have not been thoroughly explored at high temperature and pressure, which poses a related risk of H2 leakage and contamination for shallow groundwater. Some microorganisms have the ability to consume hydrogen to produce gas mixing (e.g., CH4), harmful gas pollution (e.g., H2S), and steel corrosion. This review will provide substantial information for further analyzing the scientific challenges of HGS and promoting the development of HGS simulations and practical engineering applications.