Abstract Hydrogen, as a clean and renewable energy carrier, is often considered as one of the optimal substitutes for fossil fuels, which could achieve non-polluting transportation in the field of hydrogen fuel cell vehicles (HFCVs). To bring about a guarantee in the long-distance transportation of HFCVs, the safety and ultrahigh pressure of hydrogen charge are required according to the high-pressure onboard tanks, consequently facilitating the development of compressors used in hydrogen refueling stations (HRSs). Compared with traditional mechanical hydrogen compressors, metal hydride hydrogen compressors (MHHCs) hold much more potentials due to their high security, great sealing, and lower maintenance cost. Therefore, the contents associated with MHHCs have been reported by a large number of articles, patents, and books, mainly focusing on the improvement of systematic compression ratio, the modification, and optimization of each-stage hydrogen compression material. In this review, we describe the fundamental aspects of MHHCs firstly, including the working principle of compressors, the thermodynamic and kinetic characteristics of hydrogen compression materials, simultaneously proposing an innovative three-stage MHHC design. The research progress of each-stage materials based on a three-stage MHHC is also discussed, where LaNi5-based alloys are mainly used in high-density hydrogen storage and primary hydrogen compression, while TiCr2-based alloys are considered as the candidate alloys in intermediate and final hydrogen compression. Also, ZrFe2-based alloys possessing extremely high plateau pressures, are promising in the application of the final stage. What’s more, the effects of different alloying elements on the hydrogen storage properties of TiCr2 are emphatically summarized. Finally, we also discuss the remaining challenges and look forward to the directions of emerging research for hydrogen compression materials.