Polarization of electrons arising as the result of radiation during extended motion in a magnetic field is considered. A calculation is made with the quasiclassical operator method of the probability of a radiative transition in a magnetic field with spin flip, including the case of a nonuniform magnetic field. The kinetic equation is obtained for polarization of electrons in an external field with inclusion of radiation effects, and this is used to analyze the kinetics of radiative polarization. Effects are discussed which lead to depolarization of an electron beam in motion in a nonuniform magnetic field, and means of suppressing these effects and also of intentional depolarization of a beam are pointed out. Means are discussed for measurement of the transverse polarization of high energy electrons, and a description is given of an experiment in which the first indication of the existence of the radiative polarization effect has been obtained.