The behavior of plasma in magnetic field is, as a rule, defined by nonlinear interaction of numerous oscillations and exhibits a complex turbulent pattern. Such state of plasma cannot described by linear and quasilinear theories. This paper reflects on the history of studying turbulence in magnetized plasma. In 1964, Kadomtsev (1928–1998) suggested [B. B. Kadomtsev, Vopr. Teor. Plazmy 4, 188 (1964)] that for estimation of coefficients of turbulent transport of plasma across the magnetic field, only the results of linear approximation of plasma instabilities can be used. Examples of experimental validation of the suggested approach, in particular regarding properties of turbulent positive column of discharge in a strong magnetic field, of ionization turbulence of weakly ionized plasma in crossed E, H, fields, and of turbulence of wall plasma in tokamaks, are discussed.