Cluster temperature is an important material parameter essential to many physical and chemical processes involving clusters and cluster beams. Because of the diverse methods by which clusters can be produced, excited, and stabilized, and also because of the widely ranging values of atomic and molecular binding energies (approximately from 10^-5 to 10 eV) and numerous energy relaxation channels in clusters, cluster temperature (internal energy) ranges from 10^-3 to about 10⁸ K. This paper reviews research on cluster temperature and describes methods for its measurement and stabilization. The role of cluster temperature in and its influence on physical and chemical processes is discussed. Results on the temperature dependence of cluster properties are presented. The way in which cluster temperature relates to cluster structure and to atomic and molecular interaction potentials in clusters is addressed. Methods for strong excitation of clusters and channels for their energy relaxation are discussed. Some applications of clusters and cluster beams are considered.