In this article we summarizes the work developed in the doctoral thesis “Change of conceptions of students for teachers about their management of the teaching-learning process in learning environments based on problem solving” around the concept of competence. For this reason a comprehensive review is presented from its etymology to the characterizations currently being made on this concept, particularly in mathematics education. In the first instance, the definition given initially by Chomsky (1957, 1965) and the evolution of it in works proposed by other researchers are presented. Second, there is a current consideration of competition that takes into account much of the evolution of concept presented. Finally we talk about the teaching competence and its close relationship with the management of the teaching-learning process and the changes that students have for teaching about it.