The major objective of the research described in this dissertation is the development of new laser vaporization methods for the synthesis of metal and semiconductor nanoparticles, graphene, B- and N-doped graphene, and metal and semiconductor nanoparticles supported on graphene. These methods include the Laser Vaporization Controlled Condensation (LVCC) approach, which has been used in this work for the synthesis of: (1) gold nanoparticles supported on ceria and zirconia nanoparticles for the low temperature oxidation of carbon monoxide, and (2) graphene, boron- and nitrogen-doped graphene, hydrogen-terminated graphene (HTG), metal nanoparticles supported on graphene, and graphene quantum dots. The gold nanoparticles supported on ceria prepared by the LVCC method exhibit high activity for CO oxidation with a 100% conversion of CO to CO2 at about 60 °C. The first application of the LVCC method for the synthesis of these graphene and graphene-based nanomaterials is reported in this dissertation. Complete characterizations of the graphene-based nanomaterials using a variety of techniques including spectroscopic, X-ray diffraction, mass spectrometric and microscopic methods such as Raman, FTIR, UV-Vis, PL, XRD, XPS, TOF-MS, and TEM. The application of B- and N-doped graphene as catalysts for the oxygen reduction reaction in fuel cell applications is reported. The application of Pd nanoparticles supported on graphene for the Suzuki carbon-carbon cross-coupling reaction is reported. A new method is described for the synthesis of graphene quantum dots based on the combination of the LVCC method with oxidation/reduction sequences in solution. The N-doped graphene quantum dots emit strong blue luminescence, which can be tuned to produce different emission colors that could be used in biomedical imagining and other optoelectronic applications. The second method used in the research described in this dissertation is based on the Laser Vaporization Solvent Capturing (LVSC) approach, which has been introduced and developed, for the first time, for the synthesis of solvent-capped semiconductor and metal oxide nanoparticles. The method has been demonstrated for the synthesis of V, Mo, and W oxide nanoparticles capped by different solvent molecules such as acetonitrile and methanol. The LVSC method has also been applied for the synthesis of Si nanocrystals capped by acetonitrile clusters. The acetonitrile-capped Si nanocrystals exhibit strong emissions, which depend on the excitation wavelength and indicate the presence of Si quantum dots with different sizes. The Si and the metal oxide nanoparticles prepared by the LVSC method have been incorporated into graphene in order to synthesize graphene nanosheets with tunable properties depending on graphene-nanoparticle interactions.