Appositives have been argued to provide a powerful argument in favor of a multidimensional semantics, one in which certain expressions fail to interact scopally with various operators because their meaning is located in a separate semantic dimension (as argued by Potts). On this view, appositive relative clauses and nominals have an unexceptional syntax but a semantics that radically differs from that of superficially related constructions (restrictive modifiers on the one hand, presupposition‐triggering expressions on the other) – hence the development of new semantic tools. An older line of research (due in particular to McCawley) posited instead that appositives have an unexceptional (and conjunctive) semantics, but a very nonstandard syntax; in a nutshell, the view was that even when appositives appear to be deeply embedded, they can be attached to higher propositional nodes than meets the eye. This chapter reviews the phenomenological differences between appositives and superficially similar constructions, notably restrictive modifiers, presupposition triggers, and parentheticals. It introduces accounts based on a rich semantics, in particular Potts' bidimensional framework and more recent accounts in terms of “post‐suppositions.” It revisits arguments in favor of a syntactic approach to some “wide scope” phenomena, following work by McCawley, and discusses various phenomena that have been taken to suggest that in other cases appositives can have genuinely narrow scope. It also lays out some data that suggest that sometimes the content of appositives “projects” in a nontrivial way, possibly reminiscent of presupposition projection. While the issues continue to be the object of vigorous debates, they offer a particularly interesting case study in the division of labor between syntax, semantics, and pragmatics.