We live in a rapidly changing world in which Science and Technology advance at breakneck speed, and generally speaking, the national education (mainly characterized by conservatism), remains anchored behind the societal changes. In this respect, information related to scientific cutting-edge topics as: "Nano" World, renewable energy, climate change, smart cities etc. - have small chances to be rapidly integrated into the current curriculum for Science (Physics, Chemistry, Biology) as compulsory studied subjects. The paper tries to identify the role of non-formal educational activities - mainly organized and conducted in the frame of the National Programme: "To Know More, To Be Better" ("School in Another Way") -, on familiarizing the young students with a range of cutting-edge science topics, as those activities were performed in the frame of the European FP7 Research Project called " IRRESISTIBLE - Including Responsible Research and Innovation in Cutting Edge Science and Inquiry-based Science Education to Improve Teacher's Ability of Bridging Learning Environments". (C) 2016 Published by Future Academy www.FutureAcademy.org.uk