This paper first briefly reviews the concept of intelligibility as it has been employed in both English as a Lingua Franca (ELF) and world Englishes (WE) research. It then examines the findings of the Lingua Franca Core (LFC), a list of phonological features that empirical research has shown to be important for safeguarding mutual intelligibility between non-native speakers of English. The main point of the paper is to analyse these findings and demonstrate that many of them can be explained if three perspectives (linguistic, psycholinguistic and historical-variationist) are taken. This demonstration aims to increase the explanatory power of the concept of intelligibility by providing some theoretical background. An implication for ELF research is that at the phonological level, internationally intelligible speakers have a large number of features in common, regardless of whether they are non-native speakers or native speakers. An implication for WE research is that taking a variety-based, rather than a features-based, view of phonological variation and its connection with intelligibility is likely to be unhelpful, as intelligibility depends to some extent on the phonological features of individual speakers, rather than on the varieties "per se."