Spintronics is an emerging technology that exploits the intrinsic spin of the electron and its associated magnetic moment in addition to its fundamental electronic charge. The central issue of this multidisciplinary field is the manipulation of the spin degree of freedom in solid-state systems. Discoveries in recent years have inspired a new route in spintronic research which needs no ferromagnetic components. The research field "spintronic without magnetism" is based on the possibility to manipulate electric currents via spin-orbit coupling only. The spin Hall effect (SHE) is one of the most promising effects for the generation of spin polarized currents which is even present in non-magnetic materials. The SHE appears when an electric current flows through a medium with spin-orbit coupling present, leading to a spin-current perpendicular to the charge current. In this work the SHE as well as the anomalous Hall effect (AHE) are investigated on a first principles level using the spin-polarized fully relativistic Korringa-Kohn-Rostoker Green's function method (SPR-KKR-GF) in conjunction with the linear response Kubo-Streda formalism. Intrinsic as well as extrinsic contributions to the SHE/AHE are treated on equal footing. This opened up for the first time the possibility to reliably decompose the SHE/AHE into skew and side-jump scattering as well as intrinsic contributions in a quantitative manner.