This chapter argues that a just concept of responsible research and innovation (RRI) has to be global. Three prominent definitions of RRI are surveyed to assess their suitability for globalization. The foundational principles of the von Schomberg definition (ethical acceptability, sustainability and societal desirability) are then taken forward in a comparison with the concept of inclusive innovation. Inclusive innovation is a term widely used by international agencies, such as the World Bank, and middle-income economy governments (China, India, Brazil and South Africa). Bringing out the parallels between societal desirability and inclusive innovation as well as their connection to the grand challenges of humankind leads to the conclusion that RRI can go global.