It is known since the seventies that black holes behave as thermodynamics objects and, in particular, have an entropy.
To explain the microscopical origin of this entropy is a challenge for any theory of quantum gravity. The Bekenstein-Hawking formula for the entropy of a black hole also suggests an interpretation based on a holographic principle. All these ideas nicely combine in the physics of black holes in Anti-de-Sitter space, as I will discuss in this talk. It has been a long standing problem to explain the entropy of a certain class of such black holes that naturally arise in string theory.
I will discuss recent progresses towards the solution of this problem, which involve a combination of general relativity and sophisticated quantum field theory computations.
