  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 decoherence -- the 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
quasi-normal modes or with background fields in string theory.
