Abstract During the last years the magneto-optical Kerr effect (MOKE) has received much interest because of its application to optical read-out of information stored in erasable magnetic media. Apart form this technical application it provides a helpful tool to study the electronic structure of magnetic materials. As is well known, the origin of MOKE is the simultaneous occurrence of spin-polarization in magnetic materials and of spin-orbit coupling giving rise to a non-diagonal optical conductivity tensor σ even for cubic lattices. Discussing experimental data until now one had to be content with the use of modified atomic models or with band structure calculations treating spin-orbit coupling by means of perturbation theory. To allow a reliable treatment, a description of MOKE has been developed that treats the electron-photon field interaction as well as the electronic structure of the spin-polarized system in a fully relativistic way. The approach has been implemented in connection with the recently developed spin-polarized relativistic version of the linear muffin-tin orbital (SPRLMTO) method of band structure calculation. Results of an application of our approach to ferromagnetic transition metals and alloys, as well as technical aspects of its implementation, are presented and discussed.