Both spark discharge (SD) and laser ablation (LA) techniques can be used for nanoparticle production. The major advantage of spark discharge is in the possibility of using several facilities in parallel to increase the yield of nanoparticles. To better control over this process, the mechanisms involved in both SD and LA should be examined. Here, we consider different stages involved in these processes and analyze the resulting plasma parameters. Furthermore, conditions required for nanoparticle formation are verified. First, spark discharge is considered. The results of a detailed numerical modeling are presented. The model consists of several parts: (i) streamer formation and propagation for a short gap spark discharge at atmospheric pressure. In this part, ionization kinetics and energy balance are calculated; (ii) as soon as a breakdown occurs, plasma column is formed. Joule heating of plasma and the formation of cathode layer are considered; (iii) Electrode heating and erosion take place due to ion bombardment and heat exchange with the hot plasma column. Then, laser ablation is considered. Here, again several stages are described as follows: (i) Laser energy absorption by the target; (ii) Material heating and evaporation; (iii) Plasma plume formation and its expansion in a background gas. Finally, we check conditions required for nucleation, condensation and coagulation of nanoparticles and compare both techniques.