Magnesium alloys take a special place among the hydrogen storage materials, mainly due to their high gravimetric (7.6 mass %) and volumetric (110 kg m−3) hydrogen storage capacity. Unfortunately, the kinetics of hydrogenation and hydrogen release are rather slow, which limits practical use of magnesium-based materials for hydrogen and heat storage. Refining the microstructure of magnesium alloys, ideally down to nanoscale, is known to accelerate the hydrogenation/dehydrogenation kinetics. A possible way to achieve that is by severe plastic deformation. Our first demonstration of this effect through processing of a Mg alloy (ZK60) by equal-channel angular pressing prompted a stream of further studies employing severe plastic deformation techniques to improve the hydrogen storage-relevant properties of Mg alloys. The present article provides an overview of the literature on the subject, with a natural focus on our own data.