The review considers the recording and reproduction of complete as well as partial information concerning the vector characteristics of a field. The principal methods and features of producing a complete recording of the wave polarization are indicated, namely the use of two reference beams with orthogonal polarizations, coding the reference beam with random wave fronts, and the use of three-dimensional holograms. Different aspects of the use of holographic recording of partial information concerning field polarization are considered. In such a procedure, the information on the polarization characteristics of the object wave is coded by means of other field characteristics, the amplitude and the phase. In this connection, in analogy with the phase-contrast method, the concept of polarization contrast is introduced and defined as the transformation of the changes of the state of polarization over the object into variation of the intensity of the image reconstructed from the hologram. The production of holograms by this procedure is described consistently with the aid of the correlation-matrix formalism, and also with Stokes parameters. The intensity of the virtual image is expressed in terms of the coherence matrix of the object and reference waves, or else with the aid of corresponding Stokes parameters. It is shown that the polarization state of the reference wave serves as the analyzer of the vector characteristics of the object field. The method of double exposure using orthogonally linearly polarized waves for different exposures is compared with the method of single exposure with circularly polarized fields. Certain limitations imposed on the objects and conditions of the experiment, under which both methods coincide, are indicated. Experiments with a very simple object, illustrating the procedure, are described.