Magnesium hydride has been studied extensively for applications as a hydrogen storage material owing to the favourable cost and high gravimetric and volumetric hydrogen densities. However, its high enthalpy of decomposition necessitates high working temperatures for hydrogen desorption while the slow rates for some processes such as hydrogen diffusion through the bulk create challenges for large-scale implementation. The present paper reviews fundamentals of the Mg–H system and looks at the recent advances in the optimisation of magnesium hydride as a hydrogen storage material through the use of catalytic additives, incorporation of defects and an understanding of the rate-limiting processes during absorption and desorption.