The rapid increase in recent years in the number of different digital competency frameworks, models, and strategies has prompted an increasing popularity for making the argument in favor of the need to evaluate and assess digital competence. To support the process of digital competence assessment, it is consequently necessary to understand the different approaches and methods. This paper carries out a systematic literature review and includes an analysis of the existing proposals and conceptions of digital competence assessment processes and methods in higher education, with the aim of better understanding the field of research. The review follows three objectives: (i) describe the characteristics of digital competence assessment processes and methods in higher education; (ii) provide an overview of current trends; and, finally, (iii) identify challenges and issues in digital competence assessment in higher education with a focus on the reliability and validity of the proposed methods. On the basis of the findings, and as a result of the COVID-19 pandemic, digital competence assessment in higher education requires more attention, with a specific focus on instrument validity and reliability. Furthermore, it will be of great importance to further investigate the use of assessment tools to support systematic digital competence assessment processes. The analysis includes possible opportunities and ideas for future lines of work in digital competence evaluation in higher education.