The chapter introduces the reader to the notion of the broader societal impacts of research, and to recent trends in public policy towards prioritising research that produces direct benefits to society. It explores the ‘science–society’ relationship and the obligation of publicly funded researchers to engage in science that is relevant to society at large. It compares and contrasts top-down and bottom-up approaches to defining and measuring research impacts. Examples of different European approaches to impact assessment are presented (UK, the Netherlands, Ireland, Norway). The chapter reveals the inherently political nature of defining, measuring and rewarding research impact, and what this form of science governance implies for future directions of state-funded research.