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Looking back, the debates that animated a scientific discipline often appear futile. However, the history of sampling theory is particularly instructive. It is one of the specializations of statistics which itself has a somewhat special position, since it is used in almost all scientific disciplines. Statistics is inseparable from its fields of application since it determines how data should be processed. Statistics is the cornerstone of quantitative scientific methods. It is not possible to determine the relevance of the applications of a statistical technique without referring to the scientific methods of the disciplines in which it is applied.

Scientific truth is often presented as the consensus of a scientific community at a specific point in time. The history of a scientific discipline is the story of these consensuses and especially of their changes. Since the work of Thomas Samuel Kuhn (1970), we have considered that science develops around paradigms that are, according to Kuhn (1970, p. 10), “models from which spring particular coherent traditions of scientific research.” These models have two characteristics: “Their achievement was sufficiently unprecedented to attract an enduring group of adherents away from competing modes of scientific activity. Simultaneously, it was sufficiently open‐ended to leave all sorts of problems for the redefined group of practitioners to resolve.” (Kuhn, 1970, p. 10).

Many authors have proposed a chronology of discoveries in survey theory that reflect the major controversies that have marked its development (see among others Hansen & Madow, 1974; Hansen et al., 1983; Owen & Cochran, 1976; Sheynin, 1986; Stigler, 1986). Bellhouse (1988a) interprets this timeline as a story of the great ideas that contributed to the development of survey sampling theory. Statistics is a peculiar science. With mathematics for tools, it allows the methodology of the other disciplines to be finalized. Because of the close correlation between a method and the multiplicity of its fields of action, statistics is based on a multitude of different ideas from the various disciplines in which it is applied.

The theory of survey sampling plays a preponderant role in the development of statistics. However, the use of sampling techniques has been accepted only very recently. Among the controversies that have animated this theory, we find some of the classical debates of mathematical statistics, such as the role of modeling and a discussion of estimation techniques. Sampling theory was torn between the major currents of statistics and gave rise to multiple approaches: design‐based, model‐based, model‐assisted, predictive, and Bayesian.