We are reviewing recent progress obtained in the study of hydrogen interaction with magnetic structures in rare-earth metals, emphasizing the role of the ordering state of the H-sublattice. We shall present in particular: (1) the situation in the solid solutions of the heavy rare earths, alpha*-RHx, and the efforts to relate the special quasi-unidimensional configuration of this phase (charge-density waves) to their modulated magnetism (spin-density waves) via the Fermi surface; (2) an assembly of all magnetic structures determined up to now in the heavy-RE dihydrides, beta-RH(D)(2(+x)), for a tentative comparison of the observed commensurate and/or incommensurate configurations; special mention will be made of the remarkably stable short-range ordered (SRO) magnetism always present in these systems; (3) the need for further (thorough) neutron scattering work on the magnetism in the insulating R-trihydrides, gamma-RH(D)(3(-x)), in order to specify its mechanism in the absence of RKKY exchange interaction
