Within the conditions of rapid development of internationalization processes, the scale of international cooperation between tertiary educational institutions is growing at a quick rate. Currently, the practice of international cooperation between tertiary educational institutions is the most commonly encountered in the form of: international exchange of applicants of tertiary education (students), teachers (educators), scientists; holding conferences, round tables, symposiums; exchange of information and data on improving the efficiency of the educational process. Therefore, the list of the above mentioned types of international cooperation between tertiary educational institutions is not exhaustive and is constantly updated. Based on the foregoing, the aim of the scientific article is to study the theoretical and practical aspects of international cooperation among tertiary educational institutions in the framework of determining current trends and future prospects for the development of such relations. Methods of analysis, synthesis, observation, description and comparison have been used to disclosure the theoretical and practical aspects of international cooperation among tertiary educational institutions in the framework of determining current trends and future prospects for the development of such relations. The scientific article has discussed and analyzed the dynamics of the students' mobility from abroad, enrolled in tertiary education, as well as the level of students' mobility in areas of the corresponding level of higher education in such countries, as: Germany, the Czech Republic and Sweden. The peculiarities of the functioning of the following international networks and university wide projects and platforms have been determined, namely: ACCESS, CALIE, European University Association, Eutopia, Inspireurope, International Association of Universities, MIRAI, Nordic Association of University Administrators, Nordic Centre India, Nordic Centre Fudan University, Nordic Institute of Asian Studies, SGroup European Universities' Network, SANORD, Scholars at risk, SASUF, which have been formed as a result of international cooperation among tertiary educational institutions. According to the data of the European University Association, it has been established that tertiary educational institutions of Ukraine also take an active part in the system of international cooperation. For instance, 26 tertiary educational institutions of Ukraine act as Individual Full Members and Individual Associate Members of the European University Association. It has been established that the basic areas of international cooperation among tertiary educational institutions include: the development of international mobility in the framework of the exchange not only of students, but also of educators, researchers, and administrative staff; joint teaching and investigation activities; research cooperation.