The most detailed and reliable information about the magnetic state (magnetization depth profiles) of layers can be obtained by neutron reflectometry with vector polarization analysis. Two schemes of realization of this technique are considered. Precession coils designed to manipulate the polarization vector of monochromatic beams are used in scheme I. This scheme was tested at the neutron reflectometer NR-4M (PNPI, Gatchina). The earliest experimental data on the polarization vector rotation are reported, giving direct evidence of the wave function phase shift of a massive particle, the neutron, under total reflection. The basic elements for scheme II are remanent supermirrors. This scheme is designed for use with a white beam and is advantageous for pulse neutron sources. The effect of stray fields produced by remanent supermirrors on the neutron polarization has been theoretically and experimentally evaluated; efficient ways of compensating the stray fields are proposed.