It is now part and parcel of the official philosophical wisdom that models are essential to the acquisition and organisation of scientific knowledge. It is also generally accepted that most models represent their target systems in one way or another. But what does it mean for a model to represent its target system. Surprisingly, this issue has hardly been recognised, much less seriously discussed. In the first part, I introduce the problem of scientific representation and argue for its importance. In the second part, I provide a critique of the current orthodoxy, the semantic view of theories. Though writers in this tradition do not explicitly address the issue of scientific representation, the semantic view implies that a model represents by being isomorphic or, in another version, similar to its target. I argue that this view faces insurmountable problems because both isomorphism and similarity are notions too weak to endow a model with representational power. In the third part, I develop a theory of representation that overcomes the shortcomings of the semantic view. The leading idea consists in taking representation to be explained in terms of three relations: denotation, display and designation. A model denotes its target system in roughly the same way in which a name denotes its bearer. At the same time it displays certain aspects, that is, it possesses these aspects and a user of the model thematises them. Finally, an aspect of the model designates an aspect of the target if the former stands for the latter and a specification of how exactly the two relate is provided.