This chapter presents a number of ways in which a nucleus can be produced in an excited state: stripping and pickup reactions, fission, charge exchange reactions, beta decay, Coulomb excitation, gamma absorption, inelastic electron scattering. It studies what happens to such excited nuclei as they lose their excitation energy. The various excitation mechanisms may be roughly divided into two classes, according to what kind of states they produce. In the first class, a large number of nuclear states are populated in a non-selective, random way. This produces a nucleus in or near a state of statistical equilibrium. The decay of such a state will also be described in a statistical way. The compound nucleus, introduced by Niels Bohr, is a quasi-stationary state of the nucleus where the available excitation energy is distributed statistically among all accessible nuclear degrees of freedom. The limitation of the allowed phase space is due to the ordinary conservation laws of energy, angular momentum, parity, etc.