I will explain recent results on modular, geometrically meaningful compactifications of moduli spaces of K3 surfaces, most of which are joint with Philip Engel. A key notion is that of a recognizable divisor: a canonical choice of a divisor in a multiple of the polarization that can be canonically extended to any Kulikov degeneration. For a moduli of lattice-polarized K3s with a recognizable divisor we construct a canonical stable slc pair (KSBA) compactification and prove that it is semi toroidal. We prove that the rational curve divisor is recognizable, and give many other examples.