The article aims to reveal modern state of higher education internationalization (HEI) at global and local levels. Synthesis of conceptual approaches to studying HEI allowed to concretize the meaning of HEI at modern stage in a global and institutional levels. Renovated notion has been proposed as “complete internationalization”. It is interpreted as engagement, devotion and commitment of both all education management levels and teaching stuff to multifaceted process of intentional long-lasting infusion and integration of international dimensions with comparative constituent into all functions and missions of higher education and active designing of policies, plans, programs, strategies and approaches for promotion of internationality in higher education. Due to theoretical method of conceptual and comparative analysis of research and strategic documents and the latest scientific publications on issues of global internationalization of higher education, analysis of foreign and local experience, conceptual approaches to studying HEI were depicted modern internationalization forms at global level. Interviews initiated with heads of international affairs offices enabled us to find out HEI state at local level. Questionnaires with international students, focused on likes and dislikes concerning infrastructure, teaching methods, communication with local students, future plans helped to identify the level of students’ satisfaction and attractiveness of Sumy universities. Main priorities of stakeholders are defined. Recommendations concerning further possible development of higher education internationalization are given.