Over the past three decades, research policy in the European Union (EU) has increasingly taken on board criteria of responsibility, while actively promoting research and development (R & D) activities. However, these initiatives need to be analysed in light of the way they coalesce with the prescriptive impulse of innovation, primarily conceived as a socio-economically strategic construct. The evolution and scope of responsible innovation policies may be interpreted as attempts to manage the relationships, or trade-offs, between dynamics that are more committed to economic competitiveness and those that appeal for greater openness in innovation processes. This enables us to conceive science and its relationships with society in terms of contingency, as posited in its most radical version by the responsible research and innovation (RRI) approach. However, the fact that some relationships are more resistant to change is also clear, which is expressed and justified according to an interpretation that seeks to fix boundaries for the relationships between science and society. This basic tension, and the open-and-shut dynamics associated with it, need to be addressed through an analysis of the principles, assumptions, objectives and resistances that shape the content, evolution and scope of responsible science and technology policies in Europe.