The Machine Translation course at Dublin City University is taught to undergraduate students in Applied Computational Linguistics, while Computer-Assisted Translation is taught on two translator-training programmes, one undergraduate and one postgraduate. Given the differing backgrounds of these sets of students, the course material, methods of teaching and assessment all differ. We report here on our experiences of teaching these courses over a number of years, which we hope will be of interest to lecturers of similar existing courses, as well as providing a reference point for others who may be considering the introduction of such material.