This paper presents TraMOOC (Translation for Massive Open Online Courses), a European research project developed with the intention of empowering international learners in the digital multilingual world by providing reliable machine translation (MT) specifically tailored to MOOCs from English into 11 languages (Bulgarian, Chinese, Croatian, Czech, Dutch, German, Greek, Italian, Polish, Portuguese, and Russian). The paper describes how the project is addressing the challenges involved in developing an innovative, high-quality MT service for producing accurate translations of heterogeneous multi-genre MOOC materials, encompassing subtitles of video lectures, assignments, tutorials, and social web text posted on student blogs and fora. Based on the results of a large-scale and multi-method evaluation conducted as part of the TraMOOC project, we offer a reflection on how to best integrate state-of-the-art MT into MOOC platforms. The conclusion summarizes the key lessons learned, that can be applied by the wider community of international professionals with an interest in the multilingual aspects of innovative education and new learning technologies.