After the discovery of graphene a decade ago a new emerging class of materials - twodimensional semiconductor materials (2DSCM) – has been developed. The layered structure of a lot of materials (metal chalcogenides, III-VI and II-VI semiconductors, etc.) makes it possible to grow ultrathin, so-called van der Waals heterostructures with very abrupt interfaces and low defect density and paves the way for fabricating multilayered materials with improved functionalities for novel electronic and optical devices. The unique features of 2DSCM , such as their reduced dimensionality, symmetry and appearance of topological insulator states, lead to the appearance of phenomena that are very different from those of their bulk material counterparts and these peculiarities drives new functionalities. The two dimensional nature of these materials also plays an entirely mechanical role as they are inherently flexible, strong, and extremely thin. The paper overviews several fundamental properties, preparation techniques, and potential device applications of single and few-monolayer-thick of several two-dimensional semiconductor materials. General considerations on fabrication methods and characterization of 2DSCM, its classification and analysis of the main peculiarities are presented in the first part of the paper. In contrast to graphene, the inversion symmetry is broken giving rise to a band gap opening at the K point. Furthermore, they are characterized by a strong spin-orbit interaction that can generate the appearance of the state of topological insulators. Also a strong spin-orbit interaction in combination with the circular dichroism enables selective valley and spin polarization suggesting a variety of optoelectronic and spin-valleytronic applications. Thus they have been intensively studied in the areas of lowdimension electronics, topological insulators, and valleytronics, as well as solar energy harvesting such as photolysis and photovoltaics. The second part of the paper cover a lot of recent results related to 2DSCM and nanostructures based on layered III-VI semiconductors like GaSe and InSe. Some features of intercalation method of obtaining 2DSCM nanocomposites in the form of Ga, In, Cd and Zn chalcogenide nanolamellars with nanometric sizes by heat treatment III-VI semiconductors single crystalline plates in Zn and Cd vapor are highlighted. Some aspects of structure and morphology characterization of these 2DSCM nanocomposites by different techniques are presented. Optical and photoelectrical properties of III-VI 2DSCM are revealed and a lot of peculiarities related to the transformation of electronic structure in the nanocomposites are analysed in compoarison with bulk counterparts.