The article talks about the high role of quantum chemical research methods in such a promising direction as the catalytic oxidation of saturated hydrocarbons, especially in the study of transition states of molecules. Theoretical analysis is based on research in catalysis and computational chemistry. Computational chemistry is an effective tool that allows one to calculate the structure and physical properties of catalysts, as well as the structure and energy of the activated complex. In this review, special attention is paid to identifying a sufficiently accurate and, at the same time, less energy-consuming method for determining the structure of the transition state. The most popular methods of quantum chemical calculations are presented, among which a special role is given to density functional theory (DFT), functionals B3LYP, OLYP, PBE and basis sets 6-31G, LANL2DZ. The use of machine learning by some authors, along with quantum chemical computing, to identify catalysts for activation and functionalization of C-H bonds has been mentioned. The advantages and disadvantages of computational chemistry for heterogeneous catalysis are discussed. The results of studies of catalysts predicated on transition metal complexes are summarized. It is underlined that nanocomposites based on transition metals attract the attention of researchers due to their d-orbitals, which are responsible for the reactivity when activating C-H bonds. The review also indicates plans for conducting quantum chemical calculations to study the catalytic processes of selective oxidation of n-alkanes using tran-sition metal nanocomposites as catalysts. This review will be useful for future applications of computational chemistry methods for the development of new catalysts and the study of chemical reaction mechanisms