  Various methods of obtaining longitudinally polarized positrons for future
linear colliders are reviewed. Special attention is paid to the schemes using
circularly polarized high-energy photons for positron production. Most
effectively such photons are obtained from electrons passing through a helical
undulator or colliding with a circularly polarized laser wave. Spectrum and
polarization of radiation emitted during helical motion of electrons are
considered in detail. A new simple presentation of known formulas is used to
account for the influence of the wave intensity, of the electron-beam angular
divergence, of the collimation of radiation, and of the lateral and temporal
profiles of the laser bunch on the radiation properties.
