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 the fast spinning black holes, and I will describe how recently developed techniques allow to compute the quantum corrections to the entropy of near-extremal Kerr black holes. The quantum-corrected near-extremal entropy exhibits 3/2logT behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.