The concept of responsible research and innovation (RRI) is increasingly used to describe novel ways of governing research and the relationship between key research stakeholders including researchers, industry, policy-makers and civil society. It is thus of key importance for science, research and innovation policy. This paper defines RRI as a higher-level responsibility or meta-responsibility that aims to shape, maintain, develop, coordinate and align existing and novel research and innovation-related processes, actors and responsibilities with a view to ensuring desirable and acceptable research outcomes. It shows the role privacy has in the developing framework of RRI. The paper discusses dimensions of RRI as well as weaknesses of the current approach towards RRI and provides future directions for research and practice that will allow RRI to live up to its promise and ensure that past and present work on privacy and data protection find an appropriate place within this framework.