This review article has as purpose to conceptualize the research area on teaching and learning of mathematics and to identify its problem axes. The methodology used was theoretical-descriptive of documentation-type. As a result, teaching and learning of mathematics were defined as a process intended for the appropriation of mathematical knowledge, which begins with the reflection, comprehension, construction and evaluation of didactic actions promoting the acquisition and development of skills and attitudes for a proper mathematic performance in society. Based on this concept we can identify as problem axes the difficulties, strategies, evaluation and comprehensive education based on the teaching and learning of mathematics.