Quantum mechanical equations of motion are obtained for particles and spin in media with polarized electrons in the presence of external fields. The motion of electrons and their spins is governed by the exchange interaction, while the motion of positrons and their spins is governed by the annihilation interaction. The equations obtained describe the motion of particles and spin in both magnetic and nonmagnetic media. The evolution of positronium spin in polarized media is investigated. Media with polarized electrons can be used for polarization of positronium beams.