The impact of higher education institutions on society has become the focus of significant policy engagement in recent years, most prominently as part of research evaluation. This paper presents a theoretical exploration of the notion, identifying the key dimensions as source, form, trajectory, intensity, timescale and destination. While acknowledging the importance of porosity between universities and society, and the need to address critical contemporary challenges, five shortages of the impact agenda are high: the normative dimension; the linear relationship; unpredictability; measurement; and instrumentalisation. A response to dominant conceptualisations, the paper proposals for the notion of the generative intrinsically as a more robust basis on which to base the work of tasks. The impact of higher education institutions on society has become a significant political focus in recent years, more prominently as part of research evaluation. This article presents a theoretical exploitation of the concept category, identifying the key dimensions as source, form, trajectory, intensity, time scale and destination. While recognising the importance of porosity between universities and society, and the need to address critical contemporary challenges, five dangers of the impact agenda are highlighted: the normative dimension; the linear relationship; unpredictability; measurement; and instrumentalisation. As a response to dominant perceptions, the article proposes the notion of intrinsic generative as a more robust basis on which to base the work of universities.