Devices enabling early detection of low concentrations of leaking hydrogen and precision measurements in a wide range of hydrogen concentrations in hydrogen storage systems are essential for the mass-production of fuel-cell vehicles and, more broadly, for the transition to the hydrogen economy. Whereas several competing sensor technologies are potentially suitable for this role, ultralow fire-hazard, contactless and technically simple magneto-electronic sensors stand apart because they have been able to detect the presence of hydrogen gas in a range of hydrogen concentrations from 0.06% to 100% at atmospheric pressure with the response time approaching the industry gold standard of one second. This new kind of hydrogen sensors is the subject of this review article, where we inform academic physics, chemistry, material science and engineering communities as well as industry researchers about the recent developments in the field of magneto-electronic hydrogen sensors, including those based on magneto-optical Kerr effect, anomalous Hall effect and Ferromagnetic Resonance with a special focus on Ferromagnetic Resonance (FMR)-based devices. In particular, we present the physical foundations of magneto-electronic hydrogen sensors and we critically overview their advantages and disadvantages for applications in the vital areas of the safety of hydrogen-powered cars and hydrogen fuelling stations as well as hydrogen concentration meters, including those operating directly inside hydrogen-fuelled fuel cells. We believe that this review will be of interest to a broad readership, also facilitating the translation of research results into policy and practice.