This paper provides a framework to assess the contribution of science and innovation to society. It is divided into three parts. The first part reviews the indicators of the impact of science and innovation available in the literature and explains why economic indicators dominate the field. It also discusses some exercises that try to extend the discussions and measurements of impact to more intangible dimensions, and shows that these interesting results nevertheless fail to properly address the issue. The second part develops a typology of impact covering eleven dimensions. Beyond the economic dimension, the typology concentrates on more intangible ones. Finally, in the end, the third part discusses the challenges confronting social scientists and statisticians interested in measuring the impact of science and innovation.