The European Union pushes science education to orient toward the concept of Responsible Research and Innovation (RRI; i.e., socially and ethically sensitive and inclusive processes of science and technology). Schools should further understanding on how science interacts with society and increase students' engagement in science. This exploratory study analysed concerns of 67 active, forward-looking teachers from 10 European countries using a questionnaire based on the concerns-based adoption model (C-BAM) and open-ended questions regarding the adoption of RRI into teaching. In the context of an international professional development programme on RRI, a pre/post comparison was also carried out for 29 of the teachers. The results showed that the forerunner teachers were willing to find information and collaborate on RRI teaching and believed that RRI can engage students and be a worthwhile part of the curriculum. Yet the respondents voiced personal concerns about their ability to teach RRI, and only a few concerns were resolved during the professional development period. Teachers need extended support and networking to contextualise RRI into their science lessons. On the basis of the results, we discuss the possibilities of teaching RRI implicitly rather than explicitly in order to foster students' own reasoning about RRI-related values. Our results also demonstrate that the customary questionnaire used with C-BAM gives a consistent picture of teachers' concerns but does not differentiate teachers enough in order to formulate a statistically sound clustering of concern profiles. We argue that with proper adjustments the questionnaire can provide more diverse and informative profiling of teachers' concerns.