This article explains how the "Common European Framework of References for Languages" (CEFR; Council of Europe 2001, "Common European Framework of Reference for Languages: Learning, teaching, assessment." Cambridge: Cambridge University Press) has been applied in language courses at the Language Centre (LC) of the Cyprus University of Technology (CUT), demonstrating successful adaptations, but placing particular emphasis on the challenges faced in the alignment of English for Specific Purposes (ESP) courses with the CEFR. The CEFR is a tool providing a transparent, coherent and comprehensive basis for the elaboration of language syllabuses and curriculum guidelines, the design of teaching and learning materials, and the assessment of foreign language proficiency. Its introduction has transformed the learning of languages, and its implementation requires major changes in teaching practices. The CEFR is oriented towards tasks and learning outcomes and provides descriptors of general language competence which are recognised and used internationally. However, many higher education institutions offer students the opportunity to study languages for specific purposes. In such educational contexts, the alignment of courses with the CEFR descriptors presents additional challenges. This paper demonstrates the difficulties faced by language educators at the LC of the CUT in the process of adapting a wide range of multidisciplinary English for Specific Purposes courses in accordance with the CEFR. Data were collected via focus group discussions among language educators at the LC CUT who had extensive experience in teaching ESP courses at university level. Emerging topics include stakeholders' needs analysis, materials development, effective methodologies, task design, and the use of Information and Communication Technology (ICT) tools, among others. Major findings centre on the need for a tool that would facilitate the description of ESP competence levels corresponding to the CEFR but informed by a multidisciplinary perspective.