We describe the spin-dynamics of exciton-polaritons in semiconductor microcavities in the strong coupling regime. Using the Liouville equation for the spin-density matrix in the Born-Markov approximation we obtain kinetic equations taking into account polariton-acoustic phonon and polariton-polariton scattering. We describe both the 'polariton laser' regime (non-resonant excitation) and 'optical parametric oscillator' regime (resonant excitation at the magic angle). We obtain a good agreement with experimental data on the dynamics of polarization of light emitted by microcavities.