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Background: The unique ability of carbon to form a wide variety of allotropic modificationshas ushered in a new era in material science. Tuning the properties of these materials by functionalizationis a must-have tool for their design customized for a specific practical use. The exponentiallygrowing computational power available to researchers allows for the prediction and thoroughunderstanding of the underlying physicochemical processes responsible for the practical propertiesof pristine and modified carbons using the methods of quantum chemistry. Method: This review focuses on the computational assessment of the influence of functionalizationon the properties of carbons and enabling desired practical properties of the new materials. The firstsection of each part of this review focuses on graphene with nearly planar units built from sp2-carbons. The second section discusses patterns of sp2-carbons rolled up into curved 3D structures in avariety of ways (fullerenes). The overview of other types of carbonaceous materials, including thosewith a high abundance of sp3-carbons, including nanodiamonds, can be found in the third section ofeach manuscript’s part. Conclusion: The computational methods are especially critical for predicting electronic properties ofmaterials such as the bandgap, conductivity, optical and photoelectronic properties, solubility, adsorptivity,the potential for catalysis, sensing, imaging, and biomedical applications. We expect thatintroduction of defects to carbonaceous materials as a type of their functionalization will be a pointof growth in this area of computational research.