Laves phases crystallize in simple structures and are very common intermetallic phases that can form from combinations of elements throughout the periodic table, giving a huge number of known examples. A special feature of AB2 or AB5 phases is the ability to absorb hydrogen. This study attempts to collect, systematize and summarize the knowledge about RMn₂H_x (R: Tb, Gd, Ho, Dy, Er, Sm, Nd and Y) hydrides available in the literature that is mainly related to structural and magnetic transformations. Due to the enormous wealth of data, the analysis focused on hydrides with x < 4.5 H/f.u., i.e., hydrides obtained at relatively low pressure (less than a few bars). The hydrides obtained in this way can be treated as potential hydrogen stores, which undoubtedly accounts for their current attractiveness.