Nowadays, nanostructures are one of the most investigated objects in semiconductor physics, especially Quantum confinement effect in quantum dots (0D), quantum wires (1D) and quantum wells (2D). In the case of nanostructures the energy band diagram of semiconductor has strongly changed. This leads to a crucial change of semiconductor properties such as: electrical (due to the change of free charge carrier concentration and electrons’ and holes’ mobility); optical (absorption coefficient, reflectivity index, radiative recombination efficiency); mechanical and heating properties. A new laser method elaborated for nanocones formation in semiconductors is reported. Nanocones on the surface of Ge single crystal were formed by fundamental frequency of Nd:YAG laser radiation at intensity of 30.0MW/cm2. This structure is characterized by patterns related to C6i point group symmetry covering all the surface of the sample and having translations symmetry. In the case of Si and GaAs single crystals nanocones were formed by the second harmonica of Nd:YAG laser radiation at intensity of 2.0 MW/cm2 and 5.5 MW/cm2 correspondently. The same nanostructures were formed on the surface of Si1-xGex/Si structures with x = 0.3 and 0.4 by fundamental frequency of Nd:YAG laser radiation at intensities from 2.0 till 20.0MW/cm2. The nanocones are usually formed in parallel rows on the irradiated surface with distance equal to the wavelength of laser radiation. Random distribution of nanocones is formed on the surface of Cd1-xZnxTe ternary compound with x = 0.1 by the second harmonica of Nd:YAG laser radiation at intensity within 4.0 – 12.0MW/cm2. The mechanism of nanostructures formation on the surface of semiconductors using Atomic force microscope, Electron scanning microscope, Photoluminescence and Raman back scattering methods was studied. Unique photoluminescence spectra from the irradiated surfaces of the semiconductors were found in the visible range of spectrum. Photoluminescence from Ge, SiGe/Si and GaAs nanostructures can be explained by Quantum confinement effect. A shift of micro-Raman scattering spectra in Ge and GaAs is a good evidence of this suggestion. Asymmetry of photoluminescence spectra of the irradiated SiO2/Si structure is explained by Quantum confinement effect in nanocones-nanowires with a graded decrease of diameter toward the top of nanocone. The following two-stage mechanism of nanocones formation in Si1-xGex/Si structure by laser radiation is proposed: the first stage is irradiation of SiGe/Si structure by Nd:YAG laser, which initiates Ge atoms drift to the irradiated surface due to gradient of temperature - Thermogradient effect. This process is characterized by positive feedback: after every laser pulse gradient of temperature increases due to increase of Ge atoms concentration at the irradiated surface and new Ge phase formation occurs at the end of the process. Ge atoms are localized at the surface of Si like a thin film. The second stage is formation of nanocones on the irradiated surface of the structure due to plastic deformation of Ge top layer by like Stransky- Krastanov’ mode. The “blue shift” of exciton bands in photoluminescence spectra of the irradiated Cd1-xZnxTe ternary compound is explained by Exciton Quantum confinement effect. For the first time was shown the possibility of graded band gap 1D structure formation in elementary semiconductors. Thermogradient effect has a main role in initial stage of nanostructures formation by laser radiation in semiconductors.