In this review, we focus on a small section of the extensive literature that deals with the materials containing pristine defective CNs and those incorporated in the hybrid materials. We will discuss only those topics that focus on structural defects related to the introduction of perturbation into the surface topology of a nanostructure. We focus mainly on the method using microwave (MW) irradiation, which is a powerful tool for synthesizing and modifying carbon-based solid materials. In addition, the simplicity of the technique, economy, and the possibility of conducting the reaction in solvents and solid phase, in the presence of components of different chemical nature, allows use in various combinations. In this review, we will emphasize the advantages of synthesis using MW-assisted heating and indicate the influence of the structure of the obtained materials on their physical and chemical properties. We will also highlight the role of the occurrence of defects in the carbon material and the implication in designing their properties and applications.