The ongoing quest for understanding quantum black holes is motivated
by the challenges that they pose to the basic principles of quantum
mechanics and to gravity. I will review some basic facts about the
thermodynamics of quantum black holes and the paradoxes that their
existence apparently implies. Then I will explain the consequences of
assuming that the global quantum state of the black hole and the
unitary quantum evolution operator are well defined. The results hint
towards a surprising possibility that only matter should be quantized
and gravity should not.