In this study, Fe-N-codoped carbonaceous catalysts (Fe-N-C-x) with different structures including one-dimensional carbon nanotubes (1D CNTs) and two-dimensional porous carbon sheets (2D NC) to three-dimensional carbon nanotubes/porous carbon sheets composites (3D CNTs/NC) were systematically synthesized and applied as peroxymonosulfate (PMS) activators. It was found that the Fe-N-C-x catalysts exhibited structure-dependent catalytic performance, following the order of 2D NC > 3D CNTs/NC > 1D CNTs, and also substrate-dependent degradation performance that the reaction kinetics varied greatly for different organic pollutants. Benefiting from the unique structure characteristic and high density of active sites, 2D Fe-N-C-1 showed far superior catalytic performance than the generally used carbocatalysts with negligible Fe leaching. Besides, various influential factors affecting the catalytic performance were systematically investigated. Fe-N-C-1 showed high catalytic efficiencies toward a broad spectrum of organic pollutants, and it was confirmed that both radical and non-radical degradation pathways existed during pollutants degradation. The competitive radical quenching tests and electron paramagnetic resonance measurements verified that the superoxide anion radical (O-2(<(A.-))over cap>) was the primary reactive oxidized species for degradation of p-chlorophenol (4-CP). The chronoamperometry analysis demonstrated that Fe-N-C-1 facilitated the electron transfer from 4-CP to PMS, resulting in the degradation of 4-CP through a non-radical mechanism. Our result not only reveals the structure-dependent PMS activation performance of transition-metal and nitrogen codoped carbocatalysts but also provides solid evidence that the defect-rich carbon materials with amorphous carbon and partial graphitic structure also favor the electron transfer mechanism.