I describe an algebro-geometric theory of skeleta, which provides a unified setting for the study of tropical varieties, skeleta of non-Archimedean analytic spaces, and affine manifolds with singularities. Skeleta are spaces equipped with a structure sheaf of topological semirings, and are locally modelled on the spectra of the same. The primary result of this paper is that the topological space X underlying a non-Archimedean analytic space may locally be recovered from the sheaf |∂x| of pointwise valuations' of its analytic functions in other words, (X,|∂x|) is a skeleton.