In this paper we argue that structural explanations are an effective way of explaining well-known relativistic phenomena like length contraction and time dilation, and then try to understand how this can be possible by looking at the literature on scientific models. In particular, we ask whether and how a model like that provided by Minkowski spacetime can be said to represent the physical world, in such a way that it can successfully explain physical phenomena structurally. We conclude by claiming that a partial isomorphic approach to scientific representation can supply an answer only if supplemented by a robust injection of pragmatic factors.