The ever-increasing internationalization of study programs and global mobility of students call for greater transparency of and valid information on the knowledge and skills students acquire over the course of their studies. Several theoretical and methodological challenges arise from the immense diversity of degree courses, study programs, and institutions. A recent review of the literature has revealed a substantial lack of research on assessment practices in higher education, especially on domain-specific and generic competency models, as well as on measurement methods and valid instruments for competency assessment. The German Federal Ministry of Education and Research initiated the national research program Modeling and Measuring Competencies in Higher Education (KoKoHs) to address these challenges. This article describes the assessment practices, aims, and conceptual and methodological framework of KoKoHs and presents the main results of the first funding phase of the program.