The review describes the instruments and methods of polarimetric studies that were successfully used in the Crimean Astrophysical School in the last quarter of the 20th and beginning of the 21st century. All devices described below use thes fast modulation method. They were applied to the study of various objects: classical polars, intermediate polars, other stars that have different values of circular and linear polarization, as well as a number of selected objects of the solar system, which show, among other things, a non-standard behavior of their polarization parameters. It turned out that the use of the fast modulation method made it possible to obtain statistically significant results of polarimetric measurements, even under conditions when the intrinsic variability of the object had to be detected despite a variable atmospheric transparency and other non-astrophysical factors. In many cases, the results obtained in this way were not only among the first, as in the cases of polarimetry of satellites of large planets, or some asteroids, but could not be obtained otherwise, which illustrates, for example, the result of the study of some white dwarfs and comets. A two-beam polarimeter with an acousto-optic modulator not only made it possible to obtain the most accurate polarization measurements in wide spectral bands, but also determined the strength of the magnetic field of bright stars from the observations of hydrogen lines. The five-color polarimeter remains one of the few active device in the territory of the ex-USSR, which allows obtaining spectral dependence of the polarization parameters of fairly weak objects. And various modifications of the polarimeter with a rapidly rotating analyzer were a reliable source of information on the polarization of both extremely weak and rapidly varying objects. All the experience we have gained during the operation of these devices was used in the development and creation of a multi-color two-channel polarimeter named after Nikolai Shakhovskoy. Publications based on the results of the observations by these instruments served as a ground for awarding the State Prize of Ukraine in the field of science and technology in 2010, including to the two founders of the Crimean Polarimetric School N. M. Shakhovskoy and Yu. S. Efimov.