Synthesis methods for light and radial velocity curves are currently one of the main tools for studying close binary systems (CBS). The paper gives a brief overview of the history and development of the methods and their implementations at the SAI MSU, where a set of computer programs has been created to analyze observations of various types of CBS. As a demonstration, we present the results of the analysis by our algorithms of three interesting CBSs at different evolutionary stages. An analysis of the unusual light curves of the recently discovered pre-cataclysmic binary GPX-TF16E-48 was performed using the Roche model with spots on the normal star. The X-ray light curves of the microquasar SS433 were analyzed in a model with a precessing accretion disk. Thanks to the photometric data obtained from space, the highly elliptical Wolf–Rayet binary WR22 was studied in the Roche model accounting for the absorption in the powerful wind of the Wolf–Rayet star. As a result of this detailed analysis of the light curves and involving spectroscopic information, the parameters of the CBSs and their components were found. The paper is based on a talk presented at the astrophysical memorial seminar “Novelties in Understanding the Evolution of Binary Stars”, dedicated to the 90th anniversary of Professor M.A. Svechnikov.