The Kähler?Ricci flow is a powerful parabolic tool for studying the geometry of Kähler manifolds. Its interplay with complex geometry suggests that singularity formation and continuation through singularities can be described by canonical geometric models. In this talk, I will focus on non-collapsed singularities, particularly in complex dimension two, and present a quantitative description of their geometry. I will explain how shrinking solitons, Kähler cones, and expanding solitons fit together to model the flow before, at, and after a singular time. This talk is based on joint work with Max Hallgren and Lucas Lavoyer.