In this article we provide a short review of the debate on responsible innovation and its intersection with synthetic biology, focusing on initiatives we have witnessed and been involved with in the UK. First, we describe the ways in which responsibility in science has been reconfigured institutionally, from an internal focus on the provision of objective and reliable knowledge, to a more external view that embraces the ways in which it has an impact on society. Secondly, we introduce a framework for responsible innovation as a (partial) response to this shift, highlighting its constituent dimensions and the capacities and competencies that are needed to put it into practice. Thirdly, we chart the development of social science research on synthetic biology, addressing its evolution from an 'ethical, legal and social implications' (ELSI) frame to a responsible innovation frame. Fourthly, we review findings from UK social science research with the synthetic biology community setting out challenges for productive collaboration. And finally, we conclude with suggestions on the need for changes in institutional governance.