The relevance of the study of issues related to improving the quality of education in current realities is not in doubt. One may note a wide range of opinions regarding the content and essence of this concept, its structure, ensuring the quality of the educational process, in particular, in educational institutions of higher education, and understanding of the quality of existing education by the educational process participants (teachers and students) as well as parties concerned (employers, parents, etc.). Improving the quality of education is a multifaceted and continuous process that requires careful attention from the scientific community. The authors consider the main definitions of the concept of quality of education and uncover its content. To study different views on the quality of contemporary education, several surveys of the main participants in the educational process, i.e. teachers and students, were conducted. The authors revealed the opinions of employers and graduates regarding the quality of domestic higher education and, based on these qualities, created a profile of contemporary graduates (young professionals) who have received a high- quality education. As a result of the conducted research, the conclusion is confirmed that quality is understood by each person according to their accumulated experience and the subjective idea of this category, and changes according to the requirements that are dictated by society and the state in a particular historical period, as well as depending on the conditions of the surrounding reality (a clear example is a current situation with coronavirus which shows that the main skills for employees are the skills and abilities to perform work remotely, which also become key ones when making a decision by the employer about hiring an employee).