The term „Responsible Research and Innovation (RRI)” has been increasingly used for over a decade. The RRI concept is not currently well defined. The theory of RRI is not developed enough and there are still conceptual divergences. This paper introduces the issue of Responsible Research and Innovation and addresses the following key questions: How do we define RRI? Where do we stand in terms of understanding the RRI dimensions presented in literature? What is the role of RRI in the university technology transfer activity? The study is based on literature search on the Scopus (www.scopus.com), EBSCO (www.ebsco.com), Google Scholar (scholar.google.com) and Google Books (books.google.com) databases to obtain articles published in peer reviewed journals, related to the concept of RRI and technology transfer. The search terms (for title and topic) were: responsible innovation, responsible research and innovation, RRI, technology transfer. Critical analysis of the state of knowledge allowed to propose a set of seven conceptual dimensions (inclusion, anticipation, responsiveness, reflexivity, sustainability, care and economic) of the Responsible Research and Innovation concept that may be implemented in technology transfer processes executed at universities. RRI concept is still under development. A discussion around the conceptual dimensions of RRI will be followed by the strategic challenges of universities. The study resulted in two conclusions. Firstly, the RRI concept may shift the focus of TTOs (Technology Transfer Offices) from outcomes (revenues, cash flow, rate of return, patents, license fee, etc.) to processes, which further leads to the second conclusion, that all seven presented conceptual dimensions should indicate particular types of processes in university TTO. Fulfillment of these two conclusions makes possible to implement RRI on University in a wider perspective, than just fulfill the requirements of administrative funders.