The potential of research infrastructures (RIs) to generate impacts beyond science is widely recognised by policy makers and funding agencies. Hence, the growing demand to be able to measure RIs impacts not only for research but for the society at large. The main challenges associated to this request deal with (i) the definition of RI’s impact, (ii) the identification of the variety of impacts which can be generated by RIs of different disciplines and of different types, (iii) measuring these impacts and (iv) exploring the way they are generated. This paper addresses these challenges by suggesting a possible roadmap to guide the conceptualisation and the measurement of impacts of a research infrastructure. Specifically, drawing from recent discussion on socio-economic impact assessments of RIs as well as practices of measurement of RI’s impacts, it highlights the variation of impacts which can be encountered across research infrastructures of different types and disciplines and points out to the challenges faced in measuring the different RI’s impacts.