Directional radiometry and radiative transfer: The convoluted path from centuries-old phenomenology to physical optics

•History of phenomenological radiometry and radiative transfer is described.•Fundamental weaknesses of these disciplines are discussed.•The process of their conversion into legitimate branches of physical optics is summarized.

This Essay traces the centuries-long history of the phenomenological disciplines of directional radiometry and radiative transfer in turbid media, discusses their fundamental weaknesses, and outlines the convoluted process of their conversion into legitimate branches of physical optics.