This paper summarizes the Representative Layer Theory of diffuse reflection, and contrasts it with other mainstream
theoretical approaches. A brief historical perspective is provided on the development of modeling strategies, broadly
classified as those using continuous and discontinuous mathematics. It is shown that a sample composed of a series of
distinct layers can be modeled straightforwardly and accurately using a discontinuous approach. The focus of the paper
is the Representative Layer Theory, which broadens the discontinuous modeling approach so that it is applicable to particulate samples. Experimental data validating the Representative Layer Theory is presented and the theory will be shown to explain some observed physical phenomena that were long known but not well understood. Examples are drawn from Near-Infrared Spectroscopy but the modeling approaches presented are applicable to other types of spectroscopy.