In recent years, a large number of educational systems, following the recommendations of international organisations, have introduced a competence-based emphasis into their traditionally subject-based curriculum. This move, beyond what any document can deal with, does not seem to find its way into everyday school practice easily or with instant results. This paper explores encounters and clashes between policy and practice regarding a competence-based curriculum framework. We refer firstly to the notions about information processing and digital competence held by international organisations and the Spanish and Catalan Ministry of Education, and the implications of said notions for teaching. Then, from evidence collected through class observations, interviews with students and teachers, and documents analysis in a case study, we draw on four teaching and learning scenarios where ICT is regularly used. Promoting students' digital competence is one of the key competences prescribed in the curriculum; however, our study showed that the backgrounds and educational views of teachers, as well as the teaching culture and organisation of schools, should be deeply challenged to foster this competence.