The hydrogen spillover effect (HSPE) may be involved in both hydrogen storage, an important subject for energy applications, and hydroconversion reactions over metal supported catalysts, key processes in (bio) refineries for the fabrication of high-added value chemical products. Moreover, interactions of hydrogen with solid surfaces, in the presence or not of an organic molecule, is an important topic in fundamental Heterogeneous Catalysis. Also the present talk on the HSPE may be of great interest for people involved in hydrogen energy uses or transformations of carbon feedstocks. It would also be helpful for the teaching of practical surface chemistry. Briefly, diluting the catalyst by the support leads to both increased hydrogen storage and catalytic activity. This is attributed to the so-called HSPE consisting in the dissociation of H2 on the metal particles then spreading on the support where they become either a hydrogen reservoir or active species in hydroconversion reactions. This led to debates about the conditions of observation of the effect, observation of the effect, notably the nature of the support observation of the effect, notably the nature of the support. We think that controversies about the HSPE mainly come from a misunderstanding of earlier studies (1960-1970) where the various H-adspecies on the support were not finely discriminated In this talk we critically review previous works on hydrogen spillover, focussing on characterization and reactivity of surface H atoms incorporated in metal supported catalysts in H2 or hydrocarbon + H2 atmospheres. We demonstrate that, contrary to a general belief, H stored species are not the active species in hydroconversion reactions.