After discussing a typical R-H phase diagram, some relevant examples are selected, from (i) the alpha*-RHx solid solution, (ii) the superstoichiometric beta-RH2+x dihydride, and (iii) the substoichiometric RH3-x trihydride phase. Thus, in (i) we show the influence of hydrogen upon the magnetism of Er and discuss the possible origin of the uni-dimensional configuration of the alpha*-phase; in (ii), the role of the order/disorder transformation in the excess hydrogen sublattice upon the magnetism of beta-TbD2+x and, in (iii), the electrical as well as the optical metal-insulator transitions and their relation with structural disorder in the H-sublattice. (C) 2003 Elsevier B.V. All rights reserved.