Over the last decades, digital technologies (DTs) have become ubiquitous in mathematics education. Still, their integration into classroom teaching and learning varies enormously. In this narrative overview, we focus on the different purposes for which DTs are used in mathematics education in order to study how the effectiveness of DTs depends on researchers' underlying goals and perspectives. We set up an experience- and literature-based framework including five different purposes. Applying this framework gave rise to the following results: (1) there is evidence for the benefit of using DTs for mathematics learning; (2) research on DTs leads to new theoretical developments and (3) to new design paradigms; (4) issues of equity with respect to access to and use of DTs are important but under-researched; and (5) DTs challenge curricula and teaching and assessment practices. While early research on the use of DTs focused on questions such as "does it work?" or "does it work better?", the maturing of the field has shifted to more nuanced questions. As a future research agenda, we recommend further study of how the use of DTs in mathematics education impacts the time required for learning as well as the temporality of teaching and learning, how it changes the nature of doing mathematics and the relation to basic skills and higher-order skills in particular, how curricula, teaching practices, and assessment might change due to the availability of sophisticated mathematical tools, how DTs and other resources might be combined in teaching and learning, and how they may help to address equity issues in education. These questions will prompt the development of new theoretical constructs and approaches.