Implementing innovations in mathematics education relies on scaling up professional development (PD) for mathematics teachers. Within the German Center of Mathematics Teacher Education (DZLM), the complexities involved in scaling-up processes are addressed with three implementation strategies: a material, a personnel, and a systemic strategy. For each of them, the research base is empirically established by design research and intervention studies. The "personnel strategy" focuses on preparing teachers for innovative teaching approaches and on preparing PD facilitators for conducting PDs on the content involved. The empirical research required for creating a research base for the personnel strategy investigates what teachers and facilitators need to know about their learners (students on the classroom level, teachers on the PD level) with regard to a specific (PD) content. The main focus of the "material strategy" is to provide support for teachers and facilitators by adaptable curriculum materials for classrooms and PD sessions. The empirical research on the material strategies focuses on how such material needs to be constructed to ensure both flexibility and fidelity for impactful quality implementation. The "systemic strategy" involves considering the systemic contexts on each level and cooperating with the respective stakeholders (e.g., school principals or regional PD authorities). The corresponding empirical research focuses on the interplay of processes and systemic conditions. In this paper, we present the implementation strategies on different levels, and typical research approaches and results for strengthening their empirical and theoretical bases.