Magnesium hydride owns the largest share of publications on solid materials for hydrogen storage. The “Magnesium group” of international experts contributing to IEA Task 32 “Hydrogen Based Energy Storage” recently published two review papers presenting the activities of the group focused on magnesium hydride based materials and on Mg based compounds for hydrogen and energy storage. This review article not only overviews the latest activities on both fundamental aspects of Mg-based hydrides and their applications, but also presents a historic overview on the topic and outlines projected future developments. Particular attention is paid to the theoretical and experimental studies of Mg-H system at extreme pressures, kinetics and thermodynamics of the systems based on MgH2, nanostructuring, new Mg-based compounds and novel composites, and catalysis in the Mg based H storage systems. Finally, thermal energy storage and upscaled H storage systems accommodating MgH2 are presented. •Historical overview of Mg-based hydrides.•Nanostructured Mg-based H storage materials prepared by mechanical alloying and reactive ball milling.•Thermodynamics and kinetics for Mg-based hydrides.•Catalysis in Mg-H system.•Mg-H system at high pressures: theoretical and experimental studies.