Societal engagement is a key dimension of Responsible Research and Innovation (RRI), aiming at making science, technology and innovation more transparent, interactive and responsive. Within this article, we identify and discuss the specific requirements and challenges for societal engagement under the heading of RRI along five dimensions. First, engagement aims at shaping research and innovation in a socially robust manner. Second, RRI demands a balanced representation of and a balanced view by various actor groups. Third, RRI emphasises engagement moving upstream as well as continuous engagement. Fourth, RRI focusses on forms of invited participation and calls for two-way interactions. Fifth, with the emphasis on ethics as a driving force, RRI favours specific framings of research and innovation. In conclusion, two intertwined challenges arise for societal engagement under RRI: making the political character of science and technology explicit and therefore paying particular attention to framing in 'invited participation'.