If black hole formation and evaporation can be described by an S matrix, information would be expected to come out in black hole radiation. An estimate shows that it may come out initially so slowly, or else be so spread out, that it would never show up in an analysis perturbative in MPlanck/M, or in 1/N for two-dimensional dilatonic black holes with a large number N of minimally coupled scalar fields. Alberta-Thy-24-93, hep-th/9306083. 1 Hawking’s calculation of thermal emission from a stationary classical black hole [1, 2] soon led to a major unresolved puzzle concerning quantum mechanics and gravity: what happens to a pure quantum state that collapses to form a black hole which emits approximately themal radiation? Hawking proposed [2] that the black hole would eventually disappear completely and that the resulting state of radiation, like a precisely thermal state, would be mixed. In other words, information would be permanently lost down the black hole, and there would be no S matrix to take an initial pure state to a final pure state. It was soon objected [3, 4] that this conclusion is not justified by the classical or semiclassical approximation for the black hole used to derive it, and that, in its original form at least, it violates a strong form of CPT invariance [4]. A number of alternative possibilities were given [4]. The main options now under active investigation seem to be that either most of the information comes out with the bulk of the radiation to give an S matrix [4, 5, 6, 7], or most of the information goes into a long-lived [8, 9] or absolutely stable remnant [10], or else information is lost from our universe as Hawking proposed [2]. For recent reviews of the problem, see