Ab initio methods developed within the Spin Density Functional Theory either in its Local Density Approximation (LSDA) or accounting for higher terms (GGA) are nowadays the basis for many theoretical investigations on electronic and magnetic properties of solids.

Among these, the Green's function method based on the multiple scattering theory (KKR-GF), since not requiring a translational invariance of the underlying system, is of particular flexibility. About a decade ago, this approach has been brought to a computationally extremely efficient order-$N$ form (screened KKR-GF method).

A fully relativistic implementation of this method will be presented, which allows one to account for spin polarization and all relativistic effects - including spin-orbit coupling - on equal footing. Several examples of its practical application in calculating the electronic and magnetic properties of different systems will be presented. This includes disordered systems, non-collinear magnetic configurations, supported or embedded clusters in three or two dimensions. Appropriate extensions can be made to allow for the calculation of response coefficients or spectroscopic properties.