This paper discusses a project devoted to the concept of responsibility in the field of research and innovation, which has been initiated by the European Commission in recent years (the RRI Tools project). The key element of this project is performing science with society and for society, which includes wide cooperation with different societal actors, representing researchers, business, civil society and policy makers. An important part of this concept is diversity and gender equality in the research and innovation sector. These issues are also perceived as instruments of shaping correct relationship between science and society. The paper presents the main initiatives under the Responsible Research and Innovation project and selected good practices introduced by research institutions aimed at overcoming gender imbalance in the scientific profession within the European Union.