The equations of motion for the density matrix are derived in a multiband model to describe the response of semiconductors (bulk or quantum well structures) under optical excitation with arbitrary polarization. The multiband model used, comprising the twofold conduction band and the fourfold topmost valence band (or heavy- and light-hole states), incorporates spin-splitting of the single-particle states. The interaction terms include besides the direct Coulomb coupling between carriers also the electron-hole exchange interaction, which together with the spin-splitting terms is responsible for spin relaxation. Applying the Hartree-Fock truncation scheme leads to a set of coherent semiconductor Bloch equations for the multiband case. This concept provides the theoretical frame for describing phenomena connected with optical response under excitation with arbitrary light polarization and spin relaxation: polarized optical response, polarization dynamics of VCSELs, spin relaxation, and the circular photovoltaic effect.