The use of digital tools in mathematics lessons has recently gained in significance, especially because of ongoing technical developments. Particularly in the context of mathematical modelling, digital tools have become more and more important. They have been deployed for many years and are currently being intensively discussed from a didactical point of view. This paper discusses to what extent modelling processes using digital tools can be described theoretically, and surveys significant empirical findings in this field. Based on a quantitative control study with 709 students, we especially investigated the competence of mathematising. We compared the competence development of a test-group that worked with digital tools, to a control-group that worked with paper and pencil on the same tasks during a four-lesson intervention on geometric modelling tasks. We find a comparable improvement of mathematising in both groups. This competence development was also investigated in relation to the influence of attitudes towards the software used and program-related self-efficacy. We find program-related self-efficacy, but not attitudes towards the used software, to be a significant predictor of the gain in competency. These results are discussed with respect to different performance studies examining the use of dynamic geometry software.