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REMgNi₄-based alloys, RE_(2−x)Mg_xNi₄ (RE: rare-earth metals; 0 < x < 2), with a AuBe₅-type crystal structure, exhibit reversible hydrogen absorption and desorption reactions, which are known as hydrogen storage properties. These reactions involve formation of three hydride phases. The hydride formation pressures and hydrogen storage capacities are related to the radii of the RE_(2−x)Mg_xNi₄, which in turn are dependent on the radii and compositional ratios of the RE and Mg atoms. The crystal structures formed during hydrogen absorption reactions are the key to understanding the hydrogen storage properties of RE_(2−x)Mg_xNi₄. Therefore, in this review, we provide an overview of the crystal structures in the hydrogen absorption reactions focusing on RE_(2−x)Mg_xNi₄.