Compactification of the moduli spaces of Kähler-Einstein Fano manifolds

By "adding degenerations", the moduli spaces of Kähler-Einstein (K-polystable) Fano manifolds should admit the structure of a projective variety. In this talk, I will explain the expected picture, focusing on the understood two dimensional case of Del Pezzo surfaces (joint work with Yuji Odaka and Song Sun).