Hydrides based on magnesium and intermetallic compounds provide a viable solution to the challenge of energy storage from renewable sources, thanks to their ability to absorb and desorb hydrogen in a reversible way with a proper tuning of pressure and temperature conditions. Therefore, they are expected to play an important role in the clean energy transition and in the deployment of hydrogen as an efficient energy vector. This review, by experts of Task 40 'Energy Storage and Conversion based on Hydrogen' of the Hydrogen Technology Collaboration Programme of the International Energy Agency, reports on the latest activities of the working group 'Magnesium- and Intermetallic alloys-based Hydrides for Energy Storage'. The following topics are covered by the review: multiscale modelling of hydrides and hydrogen sorption mechanisms; synthesis and processing techniques; catalysts for hydrogen sorption in Mg; Mg-based nanostructures and new compounds; hydrides based on intermetallic TiFe alloys, high entropy alloys, Laves phases, and Pd-containing alloys. Finally, an outlook is presented on current worldwide investments and future research directions for hydrogen-based energy storage.