The review aims to provide a coverage of different classes of intermetallic systems, which have the ability of absorbing hydrogen in different amounts, like binary and ternary Laves phases and Haucke-type intermetallics. Such intermetallic hydrides are attractive for applied research as potential candidates for on-board vehicular use (engines, batteries, etc.). Focus is made here on the fundamental features regarding the physical and chemical properties obtained from the first-principles e ab initio, for a better understanding of the role played by inserted hydrogen. Beside establishing the equation of state, the binding energetics, the electronic band structure, the magneto-volume effects, the hyperfine field etc., we endeavor answering the relevant question raised by solid state chemistry: “where are the electrons?”. This is approached through different schemes calling for a description of the chemical bonding, of the electron localization as well as the charge density mappings and the numerical Bader charge analysis scaling the iono-covalence of hydrogen within the lattice. For the sake of a complete scope we extend the studies to characteristics regarding the valence state changes in cerium based hydrided phases and the magnetism (spin-only, spin-orbit coupling, magnetic order of the ground state) in hydrogen modified ternary uranium intermetallics.< Leer menos