Nanoparticles have found numerous applications in such areas as photonics, electronics, medicine, etc. Further development of these fields requires reliable and versatile methods of nanoparticle synthesis with well-controlled properties. Among promising synthesis techniques, both laser ablation and plasma discharges are considered. These methods provide numerous advantages that are unique in several cases. On one hand, the main advantage of the laser ablation method is in the possibilities of changing laser parameters and background conditions and in its capacity to preserve stoichiometry. Laser-based methods also yield bio-compatible nanoparticles and nano-colloids with unique chemical properties. Laser-induced fragmentation provides additional control ways over nanoparticle sizes. To better understand and to optimize these processes, detailed numerical modeling is performed. The involved stages are considered and analyzed. The resulting nanoparticle parameters are investigated as a function of the experimental conditions. Nanoparticle properties, such as mean size and mean concentration are analyzed. Differences and similarities between the considered synthesis methods are discussed.