The binding of a dihydrogen molecule (HA to a transition metal center in an organometallic complex was a major discovery because it changed the way chemists think about the reactivity of molecules with chemically "inert" strong bonds such as H-H and C-H. Before the seminal finding of side-on bonded H-2 in W(CO)(3)(PR3)(2)(H-2), it was generally believed that H-2 could not bind to another atom in stable fashion and would split into two separate H atoms to form a metal dihydride before undergoing chemical reaction. Metal-bound saturated molecules such as H-2, silanes, and alkanes (or-complexes) have a chemistry of their own, with surprisingly varied structures, bonding, and dynamics. H-2 complexes are of increased relevance for H-2 production and storage in the hydrogen economy of the future.