For almost twenty years there has been an increasing interest in the use of nanostructured carbon materials as catalyst supports. 1-16 Following the nanotechnology wave, a wide variety of carbon nanomaterials has been investigated as catalyst supports, including fullerenes, CNTs, CNFs, carbon onions, nanodiamonds, FLG or GO. CNTs and CNFs, which constitute a new family of support offering a good compromise between the advantages of AC and high surface area graphite have been particularly studied. The main advantages offered by CNT or CNF supports are: 17 (i) the high purity of the material can avoid self-poisoning; (ii) the mesoporous nature of these supports can be of interest for liquid-phase reactions, thus limiting the mass transfer; (iii) the high thermal conductivity that limits hot-spots that can damage the catalyst; (iv) their well-defined and tunable structure; (v) their rich surface chemistry that offers numerous perspectives for adsorption and dispersion of the active phase; and (vi) the specific metal support interactions, due to high electrical conductivity of the support and to the tunable orientation of the graphene layers, that exist and that can directly affect catalytic activity and selectivity. The possibility to perform catalysis in a confined space is also of great interest. 6,18 From a theoretical viewpoint, graphene provides the ultimate two-dimensional model of a catalytic support. The reason is related to its high theoretical surface area (ca. 2630 m 2 g −1 ), high conductivity, unique graphitized basal plane structure and chemical tolerance. FLG,