  The evaporation of black holes into apparently thermal radiation poses a
serious conundrum for theoretical physics: at face value, it appears that in
the presence of a black hole quantum evolution is non-unitary and destroys
information. This information loss paradox has its seed in the presence of a
horizon causally separating the interior and asymptotic regions in a black hole
spacetime. A quantitative resolution of the paradox could take several forms:
(a) a precise argument that the underlying quantum theory is unitary, and that
information loss must be an artifact of approximations in the derivation of
black hole evaporation, (b) an explicit construction showing how information
can be recovered by the asymptotic observer, (c) a demonstration that the
causal disconnection of the black hole interior from infinity is an artifact of
the semiclassical approximation. This review summarizes progress on all these
fronts.
