The introductory article to this HSR Special Issue presents the emerging field of sociology of quantification, which can be regarded as a transdisciplinary approach to the analysis of processes of quantification. Processes of categorization and classification are included because they can result in processes of generating figures and numbers also. The contribution sketches the science-historical development of this field. It is argued that processes of quantification are related in many ways with other social and socio-economic processes. Therefore, one can speak of a comprehensive political economy of statistics, quantification and categorization. Especially the works of the French statistician and sociologist Alain Desrosières are an innovative and far-reaching groundwork for the analysis of statistics, quantification and categorization. Also, Desrosières has pointed to the fundamental role of conventions for processes of quantification (as for processes of categorization) and he has published important contributions to the French science movement of economics of convention (économie des conventions). At the end of the article, a set of positions for a sociology of quantification are presented.