The present paper discusses methods and tools for solving problems in color perception, providing an objective description of what is seen in the act of vision. A number of illustrative examples of the task of specifying low-parameter spectral descriptions providing a formal connection between radiation spaces and sensor responses are addressed. These structures are called spectral models. These are described and explained using specific examples (with analysis of the advantages and disadvantages) of their principal variants and within-type modifications. Limitations to the physical optical characteristics of scenes recorded by sensors and variants of approximations to spectral descriptions of its elements are given, along with the appropriate motivations for developing these variants, ensuring the solvability of the reverse problem thus simplified but which in the general case has no solution. In the context of the requirements for spectral models, the challenges that arise in modeling the phenomena of color constancy, as well as in setting the task of calibrating cameras, are considered. The advantages of using Gaussian spectral models (both nonlinear and multiplicatively closed) in this are discussed in comparison with optimal linear models, and three of its modifications are described which expand the color gamut, as the original version does not reproduce colors in the magenta segment. In terms of the Gaussian model with transition to the optimizing properties of the von Mises model, a method for estimating the chromaticity of a source from the color pattern of internal reflections (interreflexes) in a set of differently colored folded samples is described and shown as a result of numerical experiments (using “real” spectral data). The text combines an analysis of theoretical positions with a discussion of the results of computer simulations and physical experiments.