The energy transition is the pathway to transform the global economy away from its current dependence on fossil fuels towards net zero carbon emissions. This requires the rapid and large-scale deployment of renewable energy. However, most renewables, such as wind and solar, are intermittent and hence generation and demand do not necessarily match. One way to overcome this problem is to use excess renewable power to generate hydrogen by electrolysis, which is used as an energy store, and then consumed in fuel cells, or burnt in generators and boilers on demand, much as is presently done with natural gas, but with zero emissions. Using hydrogen in this way necessitates large-scale storage: the most practical manner to do this is deep underground in salt caverns, or porous rock, as currently implemented for natural gas and carbon dioxide. This paper reviews the concepts, and challenges of underground hydrogen storage. As well as summarizing the state-of-the-art, with reference to current and proposed storage projects, suggestions are made for future work and gaps in our current understanding are highlighted. The role of hydrogen in the energy transition and storage methods are described in detail. Hydrogen flow and its fate in the subsurface are reviewed, emphasizing the unique challenges compared to other types of gas storage. In addition, site selection criteria are considered in the light of current field experience.