After finishing secondary education in Boston (Massachusetts, USA), he enrolled in the Faculty of Medicine, from which he graduated in 1988 as the youngest doctor in the then Yugoslavia. After graduating from medical school, he went to the US, where he spent a year and received education in the field of plastic and reconstructive surgery at the Massachusetts General Hospital Clinic for Plastic Surgery, as well as the private institution for aesthetic surgery Boston Cosmetic Surgery Centre.
In 1990, after returning from the US Glumicic started working as an associate and assistant to Prof. Milojevic, MD, the doyen of aesthetic surgery in this area, at MILO, the only private aesthetic surgery clinic at the time. At the same time, he specialized in head and neck surgery and participated in all courses of the American Academy of Cosmetic Surgery, as well as the American Academy of Facial Plastic Surgery, and became their regular member. He is one of the founders and an active member of the European Academy of Cosmetic Surgery, the World Academy of Cosmetic Surgery, a member of the Croatian Society of Plastic, Reconstructive and Aesthetic Surgery, the International Society of Hair Restoration Surgery, and many other professional organizations.