The EU has authoritatively coined the concept of Responsible Research and Innovation to indicate the process by which innovators come to express responsiveness to (ethical) acceptability, sustainability and societal desirability of (the results of) their professional work (cp. Von Schomberg 2013). As a funding organisation, the EU has an interest in promoting RRI uptake in its research programs. However, both the meaning of RRI in practice and the way it can be promoted and given shape in actual Research & Development are unclear. Under Horizon 2020 a program is developed to promote RRI by developing Social Labs in which tailor-made activities will be designed together with the actors involved to make RRI fit their views and practices. This paper explores the way these Social Labs and the experiences therein can be understood, observed and comparatively assessed, and hence serve as a basis for lesson-drawing about how RRI can have an impact on R&I practices and its funding schemes. To that end, the paper defines RRI as a process by which private issues (such as technological designs or innovator choices) are redefined as res publica, that is, as affairs pertaining to the public domain. Res publica take shape via reflection on individual, ultimately private issues that are, yet, public in their consequences, and thus themselves, by coming into being, contribute to the creation of a public sphere, between the private realm and the organised collective. To make sense of the conditions under which such creation of the public sphere may take place, agency is theorized from a practice perspective. The Social Labs are understood as organised arrangements that may trigger a de-routinization of ‘objects of knowledge’ (Knorr-Cetina, 2001) so as to make them objects of representative thinking (Arendt, 1986) and subject to processes of political judgement. The paper furthermore will outline an approach to observing and assessing the experiences with the Social Lab RRI efforts based on a conceptualization of storylines as a way of producing what Hajer (1995) calls a ‘communicative miracle’, enabling actors to understand one another even in practices which are fundamentally diverse and which are characterized by discursive diversity.