The European Union (EU) encourages science education to be oriented towards the concept of Responsible Research and Innovation (RRI), i.e. socially and ethically sensitive and inclusive processes of science and technology. Connecting RRI to prevailing concepts in science education, such as the Nature of Science (NoS), may facilitate the incorporation of RRI in curricula and classrooms. We carried out a conceptual comparison between the EU’s RRI policy and a recent reconceptualization of NoS, known as the expanded Family Resemblance Approach. We discuss how the socio-institutional nature of science in that approach closely connects to the RRI and can provide a means for RRI teaching. To illustrate these opportunities, we present practical classroom approaches developed in the EU-funded project IRRESISTIBLE, and survey results on teachers’ perspectives on RRI. The aim of this work is to understand better the potential implications of RRI to research and practice in science education.