In the 1970s, when linguists began to inventory and to analyze the various forms that a presupposition can take in natural languages, their studies converged on the idea that presupposition comes under the heading of implicitness. Linguists with quite different theoretical orientations, such as Charles Fillmore (1970) or Oswald Ducrot (1972), argued that the meaning of statements contained two complementary levels of communication: the explicit, which is “illocutionary”, and the implicit, formed by the presuppositions conveyed in the statement. However, by thus anchoring presupposition in the field of implicitness, linguists carried out a profound shift in the issue raised between 1892 and 1950 by the logicians and philosophers Gottlob Frege, Bertrand Russell and Peter Strawson; as a result, this new type of questioning notably led to the scope of presupposition no longer being limited to reference to proper names and definite descriptions. A heterogeneous plethora of linguistic phenomena (several types of verbs, cleft sentences, temporal clauses, non-restrictive relative clauses, counterfactual conditionals, questions, etc.) was analyzed as types of presuppositions. In return, the notion of implicitness had to be clarified in order to become paradoxically consistent with the fact that every presupposition always explicitly appears thanks to a specific signifier in a statement’s literal form. Therefore, the theoretical assumption of construing presupposition as implicit is not obvious in itself. The purpose of our communication will be to assess the impact that this categorization had on the very fast elaboration of linguistic models (Robert Stalnaker (1973), Lauri Karttunen and Stanley Peters (1977), Deirdre Wilson and Dan Sperber (1979), ...) which, in spite of being in competition with one another, treated presupposition as a phenomenon which essentially falls within the realm of the pragmatic. To reach our aim, we will begin by identifying the various criteria that led the principal theorists to classify presupposition under the category of implicitness. This study, which will highlight the lack of consensus, will then lead us to establish a correlation between each theory’s criteria for implicitness and each one’s specific way of explaining presupposition. Finally, we will show that inscribing presupposition in the field of implicitness contributed to the massive increase of linguistic facts considered to be presuppositional in the last quarter of the twentieth century, but then curiously contributed to emptying this heteroclite grouping in favor of pragmatic analyses, highlighting, for example, that many presuppositions could correspond to conventional or conversational implicatures.