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. I will end with a brief discussion of the relevance of quantum black holes to the physics of the current heavy ion collisions at CERN.