Abstract <p>Present-day optical spectroscopy successfully solves problems of the quantitative and qualitative analysis of multicomponent mixtures of complex chemical and morphological composition. Many natural and man-made samples require direct analysis without separation into components or complex sample preparation, and often without a possibility of physical sampling. This has become possible due to technical improvements in the analytical equipment, on the one hand, and the development of mathematical methods for the analysis of multivariate data (chemometrics), on the other hand. This review considers of the most important chemometric algorithms from the viewpoint of their contributions to the creation and development of methods for the analysis of multicomponent mixtures by optical spectroscopy. Emphasis is placed on molecular spectroscopy in the ultraviolet, visible, and infrared regions, in which the accuracy and stability of the results of analysis largely depend on the mathematical apparatus used because of significant overlapping of absorption (emission) bands. Fundamental theoretical information providing a key to understanding the efficiency of the discussed methods and algorithms in constructing models for the calibration, classification, and exploratory analysis of multivariate data is also presented. Some of the presented information is reflected in the Russian scientific periodicals for the first time. Examples illustrating the use of optical spectroscopy and chemometrics for solving real analytical problems in the chemical, food, and pharmaceutical industries, ecology, and medicine without sample preparation are presented.</p>