This review considers the fundamental dynamic processes involved in the laser heating of metal nanoparticles and their subsequent cooling. Of particular interest are the absorption of laser energy by nanoparticles, the heating of a single nanoparticle or an ensemble thereof, and the dissipation of the energy of nanoparticles due to heat exchange with the environment. The goal is to consider the dependences and values of the temperatures of the nanoparticles and the environment, their time scales, and other parameters that describe these processes. Experimental results and analytical studies on the heating of single metal nanoparticles by laser pulses are discussed, including the laser thresholds for initiating subsequent photothermal processes, how temperature influences the optical properties, and the heating of gold nanoparticles by laser pulses. Experimental studies of the heating of an ensemble of nanoparticles and the results of an analytical study of the heating of an ensemble of nanoparticles and the environment by laser radiation are considered. Nanothermometry methods for nanoparticles under laser heating are considered, including changes in the refractive indices of metals and spectral thermometry of optical scattering of nanoparticles, Raman spectroscopy, the thermal distortion of the refractive index of an environment heated by a nanoparticle, and thermochemical phase transitions in lipid bilayers surrounding a heated nanoparticle. Understanding the sequence of events after radiation absorption and their time scales underlies many applications of nanoparticles. The application fields for the laser heating of nanoparticles are reviewed, including thermochemical reactions and selective nanophotothermolysis initiated in the environment by laser-heated nanoparticles, thermal radiation emission by nanoparticles and laser-induced incandescence, electron and ion emission of heated nanoparticles, and optothermal chemical catalysis. Applications of the laser heating of nanoparticles in laser nanomedicine are of particular interest. Significant emphasis is given to the proposed analytical approaches to modeling and calculating the heating processes under the action of a laser pulse on metal nanoparticles, taking into account the temperature dependences of the parameters. The proposed models can be used to estimate the parameters of lasers and nanoparticles in the various application fields for the laser heating of nanoparticles.