A variety of dimensional-structured nanocarbons were applied for the first time as metal-free catalysts to activate persulfate (PS) for catalytic oxidation of phenolics and dyes as well as their degradation intermediates. Single-walled carbon nanotubes (SWCNTs), reduced graphene oxide (rGO), and mesoporous carbon (CMK-8) demonstrated superior catalytic activities for heterogeneous PS activation, whereas fullerene (C60), nanodiamonds, and graphitic carbon nitride (g-C3N4) presented low efficiencies. Moreover, the carbocatalysts presented even better catalytic performances than activated carbon and metal oxides, such as Fe3O4, CuO, Co3O4, and MnO2. The activity of prepared rGO-900 was further competing to the most efficient electron donor of zerovalent iron (ZVI). Both characterization and oxidation results suggested that the catalytic performances of the nanocarbons are determined by the intrinsic atom arrangements of carbon hybridization, pore structure, defective sites, and functional groups (especially ...