How do models represent reality? There are two conditions that scientific models must satisfy to be representations of real systems, the aboutness condition and the epistemic condition. In this article, I critically assess the two main fictionalist theories of models as representations, the indirect fiction view and the direct fiction view, with respect to these conditions. And I develop a novel proposal, what I call ‘the new fiction view of models’. On this view, models are akin to fictional stories; they represent real-world phenomena if they stand in a denotation relation with reality; and they enable knowledge of reality via the generation of theoretical hypotheses, model–world comparisons and direct attributions.