Abstract: This paper provides a comprehensive overview of the rate-distortion-perception framework, tracing its evolution from mathematical theory to practical deployment. We review the mathematical definition of the the mathematical definition of the Blau--Michaeli function and the associated coding theorems, examine computational methods for its evaluation, and discuss alternative formulations of the framework. Operational principles and design guidelines for modern image and video coding are also presented, highlighting the rate-distortion-perception framework as a rigorous foundation for developing next-generation perceptual compression systems.