Two-dimensional materials have become one of the central research topics of scientists around the world after the production of graphene - a monatomic layer of carbon. Currently, two-dimensional crystals are among the most promising materials for next-generation nanoelectronics and photonics. The exploration of the feasibility of 2D materials devices causes a deeper insight into the physical properties of these new materials and provides a starting point for the development of a number of important practical areas. Over the past few years, researchers have been attracting increased attention from graphene-like materials of group IVA elements, such as silicene (Si), germanene (Ge), stanene (Sn), and plumbene (Pb). Experimental production and study of the unique properties of two-dimensional monatomic layers of carbon, silicon, germanium, tin and lead on various substrates created the prerequisites for the development of new generation devices based on them. The wide possibilities for controlling their exotic electronic, magnetic and optical properties through the choice of the substrate, the design and geometry of the two-dimensional layer, as well as by controlling the magnitude of elastic stresses, have made them a dominating topic for studying in the field of nanotechnology and materials sciences. This paper reviews the latest advances in growing silicene, germanene, stanene, and plumbene using epitaxial methods. Growth technologies for creation of high-quality two-dimensional structures of large area required for promising instrumentation area are considered in more details.