With the Program for International Student Assessment and Trends in International Mathematics and Science Study surveys, competency assessment became an important policy instrument in the school sector; only recently has international competency measurement gained attention in higher education with the Assessment of Higher Education Learning Outcomes (AHELO) feasibility study. As AHELO showed, measurement of competencies in higher education is a complex and multidimensional task, which poses great methodological challenges. These challenges arise out of the high diversity of degree courses, study programs, and institutions of higher education. Nevertheless, we need to address these challenges immediately if we aim to create evidence-based high-quality educational systems. This paper overviews the field of international research on competency measurement in higher education. Our analyses revealed a substantial lack of research in this area. Nonetheless, existing studies and assessment practices in various countries provide orientation on how to model competencies based on curricular and professional requirements, design assessments following the assessment triangle, and validate them comprehensively.