The international community, in the framework of the UN 2030 Agenda, has called Higher Education Institutions, to undertake appropriate actions, strategies and policies towards fulfilling the Sustainable Development Goals. However, addressing the transition to sustainability is a complex issue for Higher Education Institutions, as they follow quite diverse approaches and face several obstacles. The Sust-HEIn project (Erasmus+), which is currently running in four EU countries, proposes a new institutional model for assessing sustainability in Higher Education Institutions and aims at elevating the transition of Higher Education Institutions to green and sustainable institutions, by fostering the whole-institution approach to sustainability through systems thinking.