Display omitted •Structural defects and certain O-groups on surface of C material cause activation.•Synergistic effect takes place for heteroatomic C materials to activate persulfates.•Both radical and non-radical pathways are responsible for the activation.•Application of C materials for the activation is limited but have great potential. In recent years, persulfate-based advanced oxidation processes (PS-AOPs) for removal of organic contaminants from water have gained wide attention. Ever-emerging carbonaceous materials, including pristine carbon materials and their derivatives, heteroatom-doped carbon materials, and carbon materials with metal particles, are demonstrated to be effective in the activation of persulfates (peroxymonosulfate (PMS) and peroxydisulfate (PDS)) to generate free radicals or non-radical active species for degradation of the contaminants. In this paper, mechanisms for the activation of persulfates by carbonaceous materials and their composites are analyzed and summarized. In particular, the synergistic effect for activation improvement in the composites or in the hybrid activation systems is explored. Then the influence of the environmental conditions, such as pH, temperature, inorganic anions and dissolved organic matter, on the activation processes are discussed. Deactivation and regeneration of the carbonaceous materials are discussed as well. Finally, the application of these carbonaceous materials in activating persulfates for remediation of contaminated groundwater and treatment of wastewater are reviewed and the challenges for such applications are proposed.