Underground hydrogen storage in geologic media has gained significant interest as a strategy toward net-zero emissions. However, the selection of a feasible geologic storage medium is not a straightforward task but rather a complex function of the petrophysical and geo-mechanical characteristics of the host rock. This article, therefore, critically reviews the key elements pertinent to underground hydrogen storage along with significant recent developments. Firstly, the physical and chemical properties of hydrogen and the use of hydrogen as a fuel are introduced. Next, the trapping mechanisms pertinent to underground hydrogen storage and the factors influencing the hydrogen trapping capacity (e.g., relative permeability, capillary pressure, and wettability datasets for rock/ hydrogen /brine systems) are evaluated and their parametric trends are summarized. Other associated properties such as H-2/brine interfacial tension, hydrogen-brine diffusivity, and biological factors are also evaluated. Moreover, a detailed assessment for storage capacity, injectivity, containment, storage delivery, storage efficiency, cost, monitoring, and challenges pertinent to hydrogen storage is provided. Finally, we categorise the current research gaps and the outlook for hydrogen storage. This review thus provides a comprehensive summary of the latest developments pertaining to subsurface hydrogen storage thereby helping to de-risk the design of large-scale repositories.