After the discovery of graphene a decade ago a new emerging class of materials - two-dimensional 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, socalled 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.Transformation of a material from bulk to two-dimensional results in the realization of new physical phenomena. The resulting properties form the basis for futuristic thin film technologies. 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 several 2DSCM. 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. One of the most wellstudied families of van der Waals solids is the layered metal chalcogenides (LMDCs), the most common being MoS2. Neutral, dimensionally reduced hybrid organic/inorganic van der Waals derivatives of nonlayered solids have also recently been discovered. Dimensional reduction refers to the creation of novel crystal structures of metal-anion (M-X) frameworks. Another class of materials that can be prepared as single or few layers features bulk crystal structures are organized  into a puckered hexagonal graphene-like lattice with sp2 bonding configuration: silicene, germanene, phosforene etc.   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. In recent years there has been a revival of interest in the III-VI family of semiconductors (GaS, GaSe, GaTe and InSe) due to their exciting properties.These materials crystallize in layered crystal structure and their physical properties display a quasi two-dimensional character.Some features of intercalation method of obtaining  2DSCMnanocomposites  in the form of Ga, In, Cd and Zn chalcogenidenanolamellars  withnanometric 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 IIIVI 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.   The valence band of a variety of few-layer, two-dimensional materials consist of a ring of states in the Brillouin zone. The energy-momentum relation has the form of a “Mexican hat” or a Rashba dispersion. The two-dimensional density of states is singular at or near the band edge, and the bandedge density of modes turns on nearly abruptly as a step function. The large band-edge density of modes enhances the Seebeck coefficient, the power factor, and the thermoelectric figure of merit ZT.