Despite its being one of Roger Penrose’s greatest contributions to spacetime physics, there is a dearth of philosophical literature on twistor theory. The one exception to this is Bain (2006)—but although excellent, there remains much to be said on the foundations and philosophy of twistor theory. In this article, we (a) present for philosophers an introduction to twistor theory, (b) consider how the spacetime–twistor correspondence interacts with the philosophical literature on theoretical equivalence, and (c) explore the bearing which twistor theory (...) might have on philosophical issues such as the status of dynamics, the geometrisation of physics, spacetime ontology, the emergence of spacetime, and symmetry-to-reality inferences. We close with an elaboration of a variety of further opportunities for philosophical investigation into twistor theory. (shrink)