A research on stellar magnetism in Crimea was initiated by pioneer works of A.B. Severny, V.E. Stepanov, and D.N. Rachkovsky. Today, the study of stellar magnetic fields is a key field of research at the Crimean Astrophysical Observatory (CrAO). The 2.6 m Shajn telescope equipped with the echelle spectrograph ESPL, CCD, and Stokesmeter (a circular polarization analyzer) allows us to study the magnetic field of bright stars up to 5 m – 6 m . The Single Line (SL) technique is developed for measuring magnetic fields at CrAO. This technique is based on the calculation of the Zeeman effect in individual spectral lines. A key advantage of the SL technique is its ability to detect local magnetic fields on the surface of stars. Many results in the field of direct measurements of stellar magnetic fields were obtained at CrAO for the first time. In particular, the magnetic field on supergiants ( ǫ Gem), as well as on a number of subgiants, giants, and bright giants was first detected. This, and investigations of other authors, confirmed the hypothesis that a magnetic field is generated at all the stages of evolution of late-type stars, including the stage of star formation. The emergence of large magnetic flux tubes at the surface of stars of V-IV-III luminosity classes (61 Cyg A, β Gem, β Aql) was first registered. In subgiants, the magnetic field behavior with the activity cycle was first established for β Aql. Using the long-term Crimean spectroscopic and spectropolarimetric observations of α Lyr, the 22-year variability cycle of the star, supposedly associated with meridional flows, is confirmed. Magnetic field variability with the pulsation period was first detected for different types of pulsating variables: the classical Cepheid β Aql, the low-amplitude β Cep-type variable γ Peg, and others. In this review we cover more than a half-century history of the formation of the Crimean scientific school for high-precision direct measurements of stellar magnetic fields.