The measurement of psychological phenomena requires compliance with principles and rules established since the beginning of the 20th century and that are widely used in psychological and social research. The purpose of this article is to offer a chronological review of the basic principles and rules established from measurement theory. The methodology used was descriptive, using documentary research as a technique, through bibliographic review. The results show the rules of the numerical representation of phenomena, the mathematical principles on the notion of quantity and Campbell's (1952) measurement rules, from physics. Similarly, Stevens' (1946) measurement scales are presented as a guide for the recognition of the properties of phenomena in psychological and social research. Finally, measurement criteria and rules established from psychometrics and mathematical psychology are shown. It is concluded that the validity and rigor of the measurement are conditioned by the nature of psychological and social phenomena, as well as by compliance with a set of principles, axioms and rules from mathematics and physics.