Abstract. Black holes emit thermal radiation (Hawking effect). If after black-hole evaporation nothing else were left, an arbitrary initial state would evolve into a thermal state ('information-loss problem'). Here it is argued that the whole evolution is unitary and that the thermal nature of Hawking radiation emerges solely through decoherencethe irreversible interaction with further degrees of freedom. For this purpose a detailed comparison with an analogous case in cosmology (entropy of primordial fluctuations) is presented. Some remarks on the possible origin of black-hole entropy due to interaction with other degrees of freedom are added. This might concern the interaction with quasinormal modes or with background fields in string theory.