Objective. The purpose of the work is to determine the features of mathematical models for implementing the competence-based assessment approach. It is necessary to identify which parameters are appropriate to use in the mathematical model, the methodology for their determination, and at what stage the final assessment of competencies is formed. Method. The study is based on the theoretical and information analysis of mathematical models for assessing competencies. Result. The development of a mathematical model for assessing competencies requires taking into account factors, including the labor intensity of the academic discipline, class attendance, participation in Olympiads, conferences, etc. It has been established that competence assessment does not always depend on only one area of knowledge, but is interdisciplinary and includes not only knowledge, abilities and skills, but takes into account the influence of the social, information and intellectual environment. The study showed the prospects of applying the theory of latent variables. Conclusion. The scientific review allows developing a new mathematical model for the competence-based approach to mastering the curriculum. To modernize the competence-based approach, it is necessary to collect information on the extracurricular activities of the student. The result of the competency assessment will be a competency map, formed during the semester or course.