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13 figures.-- Supplementary information available.-- © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/, The effect of heteroatoms on hydrogen adsorption properties of activated and hybrid carbon materials is critically described. For that purpose, olive stones were activated chemically with KOH, and subsequently washed or not, and oxidised with ozone or not. Olive stones were also activated physically with CO2. A series of activated carbons prepared by chemical activation of sucrose was also investigated for comparison. As a result, many activated carbons with different pore-size distributions, surface areas, average micropore widths, oxygen contents and amounts of mineral matter could be compared. All were thoroughly characterised by adsorption of N2, CO2 and H2O, elemental analysis, XPS, thermogravimetry, and adsorption of H2 at different pressures. Many correlations between textural parameters, composition and adsorption properties could be evidenced, and were critically discussed. We show that the hydrogen uptake at 77 K is controlled by the following parameters, listed by decreasing order of importance: specific surface area, average micropore size, surface chemistry and shape of the pore size distribution. At room temperature (i.e., at 298 K), the adsorbed hydrogen uptake was in the range of 0.19–0.42 wt %; the presence of large amounts of alkali metals can further improve the hydrogen adsorption properties, but surface chemistry still has a major influence, especially through the acidic surface functions., This study was funded by the Agence National de la Recherche (ANR) from France supporting the project “Lorraine Université d’Excellence”, reference ANR-15-IDEX-04-LUE. We gratefully acknowledge the financial support of CHEERS and TALiSMAN projects, funded by FEDER.