ABSTRACT The European Union has set an ambitious target for improving energy efficiency in the building sector so that all new buildings as of 2021 should be near zero energy. A major effort is under way for the implementation of the European Directive on the energy performance of buildings (EPBD). This paper presents an overview of the relevant European legislative efforts and focuses on an example for Greece@ its national efforts to meet these objectives and an assessment of potential energy conservation in the Hellenic building stock. The untapped energy savings from the Hellenic building sector could play a major role in the efforts to reach the national indicative energy savings target of 3.8 Mtoe by 2016.