Bilingual education programmes involving English are currently experiencing an unprecedented rise in popularity, both at school and at university levels. While one of the aims of such educational programmes lies in developing both academic knowledge and language proficiency, our understanding of the interface between these two elements -- language and content -- is still developing. In this contribution I argue that one fruitful means of conceptualising this content and language interface is by focussing on disciplinary language, i.e. the language specific to a school subject or academic discipline. While the study of disciplinary literacies, with their prime consideration of reading and writing, has received some research attention (see e.g. Airey, 2011; Kuteeva & Airey, 2014), the more dynamic area of oral language in the subject classroom has been less focussed on. By drawing on an existing body of research, I show how disciplinary language within English Medium Instruction (EMI) is positioned by teachers and learners at both upper-secondary and tertiary levels of education. I place equal focus on two areas of research; firstly, I outline the perceptions of students and teachers towards (oral) disciplinary language, showing the difficulty of clearly positioning it on a continuum from 'language' to 'content' and the diverse interpretations of participants within EMI educational endeavours. The second area of research addresses student oral language production within the discipline. I show patterns of language production in terms of lexico-phraseological profiles of teacher talk and student production, as well as discourse-pragmatic analyses of patterns of argumentation and reasoning. The final section argues on the basis of these findings that EMI provides a unique potential of fostering student ability in the area of (oral) disciplinary language. Implications for practices in both secondary and tertiary EMI programmes focus on teacher education and classroom practices. [For the complete volume, "Rethinking Directions in Language Learning and Teaching at University Level," see ED594626.]