Several researchers on mathematics education seek to answer questions such as: Which is or what makes up the knowledge of the mathematics teacher? Which is the knowledge to be developed in student teachers? And, without a doubt: which are the competences of a mathematics teacher? The definitions of the terms used when answering the questions cited in the specialized bibliography on the topic are many. This article presents a revision that collects different definitions on the knowledge of the mathematics teacher, on the knowledge of the student teachers, on the competences for the mathematics teacher and on the management of the teaching-learning process. This revision is organized by presenting a chronological evolution of each of the terms. Each referring section presents a short description of the definition considered the most current, correct and complete.