Appears in collection : Balzan Conference on Open Issues in Gravitation

From the perspective of classical gravity, a black hole is the simplest object we know of. At the same time, it possesses huge entropy, hinting at an incredibly complex microstructure: understanding this fact falls in the realm of quantum gravity. In this talk I will review recent results concerning the microscopics and the thermodynamics of black holes close to extremality. In the first part, I will describe how recently developed techniques allow to compute the quantum corrections to the entropy of near-extremal Kerr black holes, both by making use of an effective near-horizon theory (Jackiw-Teitelboim gravity) and by regularizing certain zero-modes appearing in the gravitational path integral in the near horizon geometry. I then will show that the quantum-corrected near-extremal entropy exhibits 3/2logT behavior characteristic of the Schwarzian model, and predicts the lifting of the ground state degeneracy for the extremal Kerr black hole. I will then show the computation for the density of states for AdS4 black holes which admit a supersymmetric limit, and near extremal de Sitter ones.