BU/FBE is responsible for the general coordination, steering and advancement of existing PhD and/or Masters level graduate programs in 15 science and engineering areas and 4 engineering sub-areas. BU/FBE is also responsible for the design and development of new graduate programs in science and engineering.

The mission of BU/FBE is "supporting and coordinating scientific research and graduate education (in English language) in the key and pioneering areas of science and engineering, while deploying the most advanced techniques and equipment, following and contributing to the latest scientific publications and in cooperation with the international academic and scientific community".

11 areas under BU/FBE are "single discipline" areas attached to the associated 11 academic departments, while 4 are "multi-disciplinary" areas each of which is managed under the cooperation of more than one single discipline department. Additionally, there are 4 masters programs in sub-areas covered by 4 of the single discipline departments.

BU/FBE is managed and run by an Institute Director appointed by the Rector every three years (the votes cast by all faculty members of the associated 11 single discipline departments are taken into consideration in this appointment). The primary decision making body of BU/ FBE is the Institute Council, which is made up of the department heads of the 11 associated single discipline academic departments (as voting members) and heads of the interdisciplinary areas and single discipline sub-areas (as non-voting members). This council convenes at least once in every semester. The operational decisions in BU/FBE are taken by the Institute Executive Board, which is made up of the Institute Director and 5 members elected by the Institute Council. This committee meets once in every two weeks.The Institute's Secretariat is made up of the Institute Secretary and two administrative secretaries. In addition, there is a research assistant providing support in technical issues (such as web-page development/administration) and thesis evaluation.

The main management principle of BU/FBE is delegating most of the responsibility and execution regarding the main academic, research and administrative tasks such as, i) determination and revision of graduate academic programs, ii) design and development of new programs, iii) registration and delivery of courses, iv) execution and publication of research activities, v) planning, procurement and operation of research and teaching equipment and systems. In this context, BU/FBE assumes direct responsibility for coordination, control, approval, seeking new opportunities for teaching and research, information dissemination and support activities.