This review examines the processes of laser heating, melting, evaporation, fragmentation, and breakdown of metal nanoparticles, as well as the dependences and values of the threshold laser parameters that initiate these processes. Literature results are analyzed from experimental studies of these processes with gold, silver, and other nanoparticles, including laser surface melting and evaporation of nanoparticles and Coulomb fragmentation of nanoparticles by ultrashort laser pulses. A theoretical model and description of the thermal mechanisms of mentioned processes with metal (solid) nanoparticles in a liquid (solid) medium, initiated by the action of laser pulses with the threshold fluences, are presented. Comparison of the obtained results with experimental data confirms the accuracy of the model and makes it possible to use them to evaluate the parameters of laser thermal processing of nanoparticles. Applications of the processes include the laser melting, reshaping, and fragmentation of nanoparticles, the formation of nanostructures and nanonetworks, the laser processing of nanoparticles located on substrates, and their cladding on surfaces in various laser nanotechnologies. The use of laser ignition, combustion, and incandescence of nanoparticles is discussed, as is the use of nanoparticle-triggered laser breakdown for spectroscopy. These laser processes are used in photothermal nanotechnologies, nanoenergy, laser processing of nanoparticles, nonlinear optical devices, high-temperature material science, etc. In general, this review presents a modern picture of the state of laser technology and high-temperature processes with nanoparticles and their applications, being focused on the latest publications with an emphasis on recent results from 2021–2024.