This review discusses the various preparation methods and physicochemical properties of highly porous carbons derived from metal-organic frameworks (MDCs) or covalent organic frameworks (CDCs). It also explains the roles of physical and chemical activation processes in the preparation of MDCs/CDCs with tailored physicochemical characteristics. The carbonization and activation parameters that control (i) the formation of pores (micropores, mesopores, or macropores), (ii) carbon yield, (iii) the incorporation of heteroatoms (N, S, O, P, metal, etc.), (iii) morphology, and (iv) the hydrophobicity of MDCs/CDCs are explained systematically. Importantly, the physicochemical properties of MDCs/CDCs are compared with those of conventional carbons to highlight the advantages of these materials. Additionally, the applications of MDCs/CDCs in the adsorptive removal of typical hazardous organics, such as pharmaceuticals, personal care products, phenolics, pesticides, dyes, and aromatics from water, are reviewed. The adsorption results are also compared with those of conventional carbons to demonstrate the superior performance of MDCs/CDCs in liquid-phase adsorption. These results are explained in terms of maximum adsorption capacities, adsorption mechanisms, and reusability. Finally, this review provides research outlooks for readers in the relevant fields.