I'll present a general theory of "tropical schemes", or skeleta, which is based on reversing the correspondence that associates to a "tropical object" its semiring of convex piecewise-affine functions; in this way, we can understand, and generalise, certain classical constructions using semiring theory. For example, we can recover the dual intersection complexes of degenerations of varieties as skeleta. This construction is naturally intertwined with the theory of non-Archimedean geometry.