In this talk, I will explain how to compactify moduli spaces of polarized K3 surfaces, and describe the singular objects (KSBA stable pairs) at the boundary. For the Deligne-Mumford compactification of the moduli space of genus g curves, the boundary strata are encoded by certain "cartoons": genus g stable graphs. For K3 surface pairs, the boundary strata are rather "polarized" integral-affine structures on the two-sphere, and their combinatorial types are governed by an object called a semifan. This is joint work with Valery Alexeev.