Interest in entrepreneurship among students is growing quickly, and the number of programs devoted to it is increasing. Due to their roles as centers where education, research, and knowledge production occur, higher educational institutions (HEIs) can provide diverse formal and informal learning opportunities to develop entrepreneurial mindsets and skills. However, despite its long history and popularity, further research is still needed to consider the different understandings and terminology, the philosophical foundations, and the content and methodological questions regarding entrepreneurship education. The purpose of this paper is twofold. First, it aims to highlight and identify the main trends in entrepreneurship education development based on a qualitative comparative analysis of six Hungarian and thirty-six international master’s degree programs in Entrepreneurship and Innovation. By investigating the target groups, learning objectives, program structures, curricula, and learning activities of these master’s degree courses, similarities and differences in the assumptions on the key components of entrepreneurship as competence and the best practices can also be identified. Second, the study attempts to contribute to the existing knowledge base of entrepreneurship competence analysis by exploring the perception of entrepreneurship among a group of Hungarian experts representing the labor market. The relative importance of entrepreneurial skills and competencies and the characteristic patterns of the opinions are defined by Q-sort evaluation. While the analysis can be acknowledged as a pilot study, key findings can provide valuable inputs for HEIs to offer diverse formal and informal learning opportunities to develop entrepreneurial mindsets and skills.