Abstract:Sympathetic cooling is based on taking energy from certain particles (atoms, molecules or clusters) by a relatively cold environment ('reservoir') that holds the thermal contact with the cooled objects. This method of decreasing the energy is more flexible to compare with other ways: laser cooling, evaporative cooling, etc. Sympathetic cooling can be useful to prepare qubits for quantum computing and to make an efficient cooling of large molecules (like benzene) and Bose-condensates. The great progress has been achieved recently in ultracold collisions for some atoms (rubidium, strontium, lithium, cesium), alkali metal dimmers, NH molecules. We will make a summary of some methods for sympathetic cooling of neutral particles, its progress and perspective; and present a simple qualitative model to estimate the basic parameters of the process.