Quantitative approaches to information recovery from black holes
  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. 
Vijay Balasubramanian and Bartlomiej Czech
hep-th