The binding of a dihydrogen molecule (H2) 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 H2 in W(CO)3(PR3)2(H2), it was generally believed that H2 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. Metalbound saturated molecules such as H2, silanes, and alkanes (-complexes) have a chemistry of their own, with surprisingly varied structures, bonding, and dynamics. H2 complexes are of increased relevance for H2 production and storage in the hydrogen economy of the future.