This chapter outlines a vision behind responsible research and innovation (RRI), taking a largely European policy perspective. It provides a definition of the concept and proposes a broad framework for its implementation under research and innovation schemes around the world. The author makes the case that RRI should be understood as a strategy of stakeholders to become mutually responsive to each other, anticipating research and innovation outcomes aimed at the “grand challenges” of our time, for which they share responsibility. Research and innovation processes need to become more responsive and adaptive to these grand challenges. This implies, among others, the introduction of broader foresight and impact assessments for new technologies, beyond their anticipated market‐benefits and risks.