The aim of this paper is to provide an analysis of modality by means of the existence of concrete impossible worlds. In particular, I pursue a strategy according to which logical impossibility is analyzed as logical inaccessibility. I then consider whether it makes sense to think of logical models in isolation from the concrete world but without their being divorced from all spatiotemporal totalities. The metaphysics of structure developed in this paper assumes that structural properties of possible and impossible worlds are primitive and objective. However, I provide some characterizations of their logical and metaphysical behavior, as well as guidelines for talking about them