Underground hydrogen storage (UHS) is a promising solution to meet the increase in energy supply and demand while supporting the energy transition to net-zero carbon. The successful implementation of UHS requires careful assessment of several scientific aspects, among them evaluating the cement stability and wellbore integrity to ensure safe storage and production of hydrogen. Few studies have evaluated the geochemical reactivity of cement to hydrogen; however, more studies are needed to explore the role of hydrogen adsorption and diffusivity behavior with cement and address the associated wellbore integrity issues. This minireview presents the state-of-the-art advancement in evaluating the impact of hydrogen on cement wellbore stability from various aspects, including hydrogen/ cement interactions, hydrogen adsorption and diffusivity, current methodologies, experimental setups, and the role of cement additives and cushion gases. This minireview provides a general comparison between UHS and other gas storage applications and mainly aims to bridge the knowledge gap by providing insights for practical implementations, challenges, and future directions relevant to wellbore integrity. Although most of the reviewed studies reported a low impact of hydrogen injection on cement stability, the successful implementation of UHS requires further assessment as various technical and non-technical factors and mechanisms are involved. Systematic scientific studies should be performed in the future, which will assist in overcoming the existing challenges and reducing the uncertainty associated with wellbore integrity during UHS.