The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in action in the physical and social world, and the predicative form of knowledge, which consists in the linguistic and symbolic expressions of this knowledge. As it deals with the progressive complexity of knowledge, the conceptual field framework is also useful to help teachers organize didactic situations and interventions, depending on both the epistemology of mathematics and a better understanding of the conceptualizing process of students.