The classical theorem of Neukirch and Uchida says that number fields are completely determined by their absolute Galois groups. In this talk we’ll explain joint work with Clark Barwick and Saul Glasman that gives a version of this reconstruction result to schemes. Given a scheme X we construct a category Gal(X) that records the Galois groups of all of the residue fields of X (with their profinite topologies) together with ramification data relating them. We’ll explain why the construction X ↦ Gal(X) is a complete invariant of normal schemes over a number field. The category Gal(X) also plays some other roles. For example, its classifying space recovers the étale homotopy type. We’ll also discuss some applications of this new perspective on the étale homotopy type.