The speaker will talk about geometric compactifications of moduli spaces of K3 surfaces, similar in spirit to the Deligne-Mumford moduli spaces of stable curves. Constructions borrow ideas from the tropical and integral-affine geometry and mirror symmetry. The main result is that in many common situations there exists a geometric compactification which is toroidal, and many of these compactifications can be described explicitly using tropical spheres with 24 singular points. Much of this talk is based on the joint work with Philip Engel.