  The formation and evaporation of a black hole can be viewed as a scattering
process in Quantum Gravity. Semiclassical arguments indicate that the process
should be non-unitary, and that all the information of the original quantum
state forming the black hole should be lost after the black hole has completely
evaporated, except for its mass, charge and angular momentum. This would imply
a violation of basic principles of quantum mechanics. We review some proposed
resolutions to the problem, including developments in string theory and a
recent proposal by Hawking. We also suggest a novel approach which makes use of
some ingredients of earlier proposals. [Based on Talks given at ERE2004 "Beyond
General Relativity", Miraflores de la Sierra, Madrid (Sept 2004), and at CERN
(Oct 2004)].
