In the paper, the author takes stock of the conceptual reflection and empirical studies described in the current scientific literature on responsible innovation in the context of the emergence of Responsible Research and Innovation (RRI) concept. RRI has been promoted in the European Union as a part of the Europe 2020 strategy with the objective of making research and innovation more sustainable and inclusive. As more than half of the EU’s firms declare conducting innovation activities RRI problematic becomes more relevant than ever. There remain many open questions, unresolved dilemmas and empirical white spots that call for more research in this field. This paper’s main focus is the problem of RRI acceptance as a global framework for responsible innovation and the scarcity of suitable instruments that may help industry understand and adopt this concept. The main contribution of this paper are: the critical analysis of the RRI concept and its implications for industry, proposing a concept of RRI index for innovating enterprises.