Carbon-based nanomaterials have been verified experimentally and theoretically as a kind of good catalysts in both heterogeneous reactions and electrochemistry.Therein,graphene,carbon nanotubes(CNTs),porous carbon,heteroatom-doped carbon and supported carbon are studied extensively.Based on the molecular modeling methods including quantum mechanics,first principle method and molecular dynamics,the correlation between the macro-performance and the micro-structure is being clearly interpreted step by step.Nevertheless,it remains ambiguous when it comes to some specific problems.For example,it is debatable for the activity origin of carbon-based catalysts in the oxygen reduction reaction(ORR).As a novel metal-free catalyst differing from metallic materials,it is challenging but critical to figuring out the restraint factors from atomic and electronic levels,which can guide the structural design of carbon-based catalysts with high chemical and/or electrochemical activity and stability.