Main Topics You Can Find in this “ICME-13 Topical Survey” -- Introduction -- Survey on the State-of-the-art -- Summary and Looking Ahead.Open AccessThis ICME-13 Topical Survey reviews the state-of-the-art by first exploring the roots and scope of design science. Second, it presents two examples of current design science projects that focus on substantial learning environments including a student and a teacher perspective. Subsequently, the book elaborates on how empirical research can be conceptualised within design science. Lastly, it explores developments in design science from a national and international perspective, while also discussing current trends in design research. Within the German-language tradition, considering ‘mathematics education as a design science’ primarily draws on the works of Wittmann. The core of this approach constitutes designing and investigating learning environments that involve substantial mathematics.