Roles of the hydrogen atoms attached to the metal center of transition metal polyhydride complexes, L_nMH_x (x ≥ 3), are analyzed for about forty types of organic reactions catalyzed by such class of species. Reactions involve nearly every main organic functional group and represent friendly environmental procedures of synthesis of relevant and necessary molecules in several areas ranging from energy and environment to medicine or pharmacology. Catalysts are mainly complexes of group 8 metals, along with rhenium and iridium, and manganese and cobalt to a lesser extent. Their MH_x units can be formed by Kubas-type dihydrogen, elongated dihydrogen, or hydride ligands, which facilitate both the homolytic and heterolytic σ-bond activation reactions and hydrogen transfer processes from the metal center to unsaturated organic molecules. As a consequence of the ability of polyhydride complexes to activate σ-bonds, the vast majority of the reactions catalyzed by derivatives of this class involve at least one σ-bond activation elemental step, whereas two sequential ruptures of σ-bonds and the cross-coupling of the resulting fragments take place in a variety of reactions of C–H functionalization and hydrodefluorination. The hydrogen transfer processes usually generate highly unsaturated metal fragments, which are very reactive and extremely active in interesting C–C coupling reactions. Polyhydride complexes bearing Kubas-type dihydrogen ligands are the last intermediates in dehydrogenation processes, while they can be the first ones in hydrogenation reactions. Polyhydrides coordinating elongated dihydrogen ligands are acidic, while classical hydride complexes behave as Brønsted bases. The combination of the properties of both types of species in a catalytic cycle gives rise to interesting outer-sphere processes. The basic character of the classical hydride ligands also confers them the ability of cooperating in the coordination of acidic molecules such as boranes, which is of great relevance for reactions involving the activation of a B–H bond. Multiple bonds of unsaturated organic molecules also undergo insertion into the M–H bond of the catalysts. Such insertions are a key step in many processes.