Abstract Nowadays, two-dimensional crystals (2D materials) and structures with quantum dots (0D materials) are considered as one of the most promising materials for electronics and photonics of the next generation. The basic method of synthesis of heterostructures with 2D and 0D structures is their self-induced formation during the molecular beam epitaxy. Three epitaxial growth modes are distinguished: Frank–van der Merwe, Volmer–Weber, and Stranski–Krastanow, that allow one to obtain multi-layered structures with 2D materials, quantum wells and quantum dots. In this work generalized kinetic model of epitaxial growth of nanostructures by all three mechanisms is presented. Comparison of various growth modes is conducted and their peculiarities are pointed out. Ways to control the properties of obtained 2D and 0D nanostructures are proposed with the help of the established model.