In European science and technology policy, various styles have been developed and institutionalised to govern the ethical challenges of science and technology innovations. In this paper, we give an account of the most dominant styles of the past 30 years, particularly in Europe, seeking to show their specific merits and problems. We focus on three styles of governance: a technocratic style, an applied ethics style, and a public participation style. We discuss their merits and deficits, and use this analysis to assess the potential of the recently established governance approach of 'Responsible Research and Innovation' (RRI). Based on this analysis, we reflect on the current shaping of RRI in terms of 'doing governance'.