Programming and computational thinking have (re)gained an increased focus in compulsory education worldwide, consequently demanding teachers of various subjects to engage in the teaching and learning of the two. A recent curriculum reform in Norway emphasised the development of students’ computational skills by integrating programming into four subject domains: mathematics, natural science, music, and arts and crafts. However, these requirements come without a necessary professional development programme and are based on the presumption that all concerned teachers understand the concepts of programming and computational thinking and know how to teach these skills in a sound pedagogical and didactical way. Therefore, this study investigated how teachers understand programming and computational thinking and the relationship between the two concepts. We also investigated the teachers’ approaches to teaching these concepts and their need for further professional development. To address these issues, we conducted semi-structured interviews with eight primary school teachers and thematically analysed the data. Overall, the teachers reported positive attitudes towards the new curriculum and its focus on 21st-century skills, including programming and computational thinking. However, their understanding of these concepts was narrow, focused on only one of the six pertinent subskills: algorithms. Furthermore, the teachers’ teaching approaches were limited. Finally, we observed a variety of professional development processes and practices. The teachers accentuated a critical need for professional development within these domains. Our findings showed that to fulfil the curricular expectations of developing students’ computational thinking skills, increased training of primary school teachers is needed.