Around four decades ago, David Collingridge put forward a dilemma that has been widely adoptedamongst the technology assessment (TA), and later, responsible research and innovation (RRI) communities. The so-called Collingridge dilemma has permeated discussions on the governance of science, technology and innovation, enclosing an enormous challenge: that of anticipating their potential consequences and controlling emerging technologies. In this paper, we outline and reflect on some of the key challenges that influence the development and uptake of more inclusive and responsible forms of science, technology and innovation. Our analysis draws on a large body of empirical and theoretical research done by the different authors to reflect on challenges emerging from the complex and diverse organisational characteristics of universities, the enactment of responsibility in the private sector, the emergence of bottom-up, grassroots innovation and the hidden dimensions of sustainability, equity and transdisciplinarity. Taking these together, we paraphrase Collingridge’s famous dilemma of social control of technology to introduce a complementary dilemma which might be useful in the study of RRI, that of ‘societal alignment’ in science, technology and innovation. The dilemma of social alignment differs from that of control in at least five dimensions: a) the epistemic communities involved, b) governance mechanisms, c) ‘nature’ of the problem, d) backward or forward looking focus and e) scale and scope of sociotechnical systems. By starting to unpack this concept, we outline an agenda that remains scattered and overlooked among some communities in the field of the governance of research and innovation.