This chapter describes the evolution of Responsible Innovation (RI) and Responsible Research and Innovation (RRI) as two significant discourses emerging over the last decade. RI is a discourse with strong academic roots. Anchored in a future-oriented notion of responsibility, it envisions the integration and embedding of capacities for anticipation, reflexivity, inclusive deliberation and responsiveness in and around the processes of innovation and techno-visionary science aimed at this. RRI emerged in contrast as a policy discourse from the European Commission's Science in Society programme. While its early formulation shared much with the discourse of RI, over time it has become more instrumentally and prosaically framed around a package of five 'EC RRI' keys - gender, ethics, public engagement, open access and science education. After analysing and critiquing the main features of these discourses we consider their translation into policy and practice, before concluding with research gaps for future study.