Logical anti-exceptionalism has been frequently defined on negative terms: it is a view according to which logic is not an exceptional discipline. More positively, anti-exceptionalism sees logic as similar to other empirical sciences. That leaves a lot of space to characterize what the view actually (positively) amounts to. We propose that one fruitful way to do that is through the so-called ‘logic as models’ view. One of the benefits of doing so concerns the crucial notion of a true or right logic. By framing anti-exceptionalism in terms of models, we are in a better position to borrow from the philosophical literature on models to articulate views of how a model/theory relates to its target, accounting for what sense can be made of the very idea of a correct theory. We discuss two such accounts, and how anti-exceptionalism may be impacted by them.