To assess the effectiveness of teachers and teaching, it is necessary to develop an appropriate understanding of what makes a “good” teacher. According to the framework by Medley, this includes amongst others focusing on the knowledge, skills, and values that a teacher possesses. To appropriately describe these competencies, current research departs from a broad conceptualization of competence that includes dispositional aspects, such as mathematical content knowledge, pedagogical content knowledge, and general pedagogical knowledge. Furthermore, situation-specific skills that are related to school practice such as the perception of instructional quality, interpreting, and decision-making are considered. The chapter gives an overview of different conceptualizations of teachers’ professional competence used in mathematics education studies and describes the evolution of research on mathematics teachers’ competence over the last three decades. It concludes with theoretical and methodological challenges that research in this field focuses on today.