In the 1970s, Michel Foucault made the bold assertion that population emerged suddenly in the eighteenth century as an object of knowledge to be controlled by a set of ‘biopolitical’ practices. While Foucault’s disruptive claims have been seriously tempered by historians, there is no doubt that the idea of population was debated and burnished during the eighteenth century. This essay reviews the literature on these matters and explores the central role of quantification in the development of biopolitics, especially in discussions of infant and maternal mortality in France and Britain. It discusses the writings of Thomas Robert Malthus and political economists and their stimulation of national censuses and civil registration offices, but stresses that the statistical concept of population was not solely a product of state power; it emerged also in British voluntary hospitals, and hospital medicine importantly exploited quantification to identify and evaluate different populations of patients. The disciplines of probability and statistics, public health, vital statistics and demography developed as both social sciences and tools of governance.