▪ Abstract  We review the propagation of energetic partons in hot or cold QCD matter, as known from recent work. We summarize advances in the understanding of both collisional and radiative energy loss. Our emphasis is on radiative energy loss, which has very interesting properties that may help to detect the quark-gluon plasma produced in heavy-ion collisions. We describe two different theoretical approaches, which lead to the same radiated gluon energy spectrum. The case of a longitudinally expanding QCD plasma is investigated. The energy lost by a jet with given opening angle is calculated with the aim of making predictions for the suppression (quenching) of hard jet production. Phenomenological implications for the difference between hot and cold matter are discussed. Numerical estimates of the loss suggest that it may be significantly greater in hot matter than in cold. This makes the magnitude of the radiative energy loss a remarkable signal for quark-gluon plasma formation.