  The quantum theory of black holes has opened up a window to study the
intersection of general relativity and quantum field theory, but perceived
paradoxes concerning the fate of classical information directed at a black hole
horizon, as well as concerning the unitarity of the evaporation process, have
led researchers to question the very foundations of physics. In this
pedagogical review I clarify the ramifications of the fact that black holes not
only emit radiation spontaneously, but also respond to infalling matter and
radiation by emitting approximate clones of those fields in a stimulated
manner. I review early purely statistical arguments based on Einstein's
treatment of black bodies, and then show that the Holevo capacity of the black
hole (the capacity to transmit classical information through a quantum channel)
is always positive. I then show how stimulated emission turns the black hole
into an almost optimal quantum cloning machine, and furthermore discuss the
capacity of black holes to transmit quantum information. Taking advantage of an
analogy between black hole physics and non-linear optics I show that a
calculation of the evolution of a black hole over time, using a discretization
of the black hole $S$-matrix path integral, yields well-behaved Page curves
suggesting that black hole evaporation is unitary. Finally, I speculate about
possible observable consequences of stimulated emission of radiation in black
holes.
