Carbon materials have shown a great potential in the academic field and have been employed for plenty of applications. Graphene, a natural two dimensional polymer, and carbon nanotube (one dimensional analog) are meritorious candidates with fascinating physicochemical features. However, a chemical process is needed in order to customize their properties toward desired applications. Among different methods, covalent functionalization is the most promising approach for this purpose. On the other hand, the natural 2D polymer (graphene) inspired researchers to design and synthesize other 2D polymers. Nevertheless, the synthesis of 2DPs is still in its early stage and there is plenty of space for improvement in this field. Consequently, to expand these fascinating materials we conceived a new idea to functionalize graphene/carbon nanotube and synthesis of a 2D polymer by a new method. Scientific contribution of the thesis is in three main directions, which are addressing mentioned challenges for carbon nanotubes, graphene and 2D polymers. In the first part we intend to investigate a controlled, reproducible, and mild covalent functionalization of graphene by a one-pot reaction between triazine and sodium azide to generate dichlorotriazine intermediate which could provide a selective and controlled modification approach through substitution the reactive chlorine of the triazine groups. The different reactivity of chlorine allows us to perform stepwise post-modification on graphene by manipulating the temperature from 25 up to 65 °C. As a result, defined bifunctional 2D nanomaterials (graphene) were provided and covered with hyperbranched polyglycerol (hPG) in a controlled and stepwise manner. In the second part we intend to design and establish a new nondestructive covalent method to functionalize CNTs. We explored unique non-destructive covalent, gram-scale functionalization for CNT by a new nitrene [2+1] cycloaddition. By this method the reaction between CNT and dichlorotriazine intermediate resulted in dichlorotriazine functionality that rebuilds the extended π-system of CNTs, thereby preserving opteoelectronic properties of carbon nanotube. Lastly, the challenge of in-solution synthesis of a 2D polymer was investigated and a new nanostructure was prepared. We introduced a metal-assisted method, in which calcium carbide and triazine are monomers and dimethylformamide is the solvent. This reaction was directed in two dimensions by calcium ions derived from calcium carbide and induced 2DTHs with amorphous structures. Calcium ions coordinated with nitrogen atoms of triazine (ligand-metal interaction), which prevented bond rotation and provide enough rigidity for the desired 2D 193 structure. We investigated the chemical structure and physicochemical properties of the obtained 2D structure and evaluated the mechanism of the related reactions. Based on our investigations, the water content of the reaction medium was one of the crucial factors that affected the structure of the product dramatically. While pure 2DTHs were obtained under dry conditions, graphite/2DTHs mixture or even pure graphite was obtained by increasing the water content of the reaction medium. Taking advantage of their straightforward and gram-scale synthesis as well as fluorescence, photothermal and photodynamic properties, the synthesized two-dimensional triazine heterostructures are promising materials for a wide range of future applications.