The aim of magnetoelectronics is to design magnetic storage devices of smaller size, microchips on a magnetic basis, exploitingbesides the charge also the spin degree of freedom. A prominent example is the tunneling magnetoresistance (TMR).The interesting task of the theory lies in explaining the experimental observations, the more thrilling task is the investigation of theproperties of novel devices and the design of these devices itself. For the proper functioning of a magnetic device the direction of the spontaneous magnetization (the easy axis) and the energy required toalter the magnetization direction, the so-called magnetic anisotropy energy (MAE), has to be known. The origin of this anisotropy is the interaction of the magnetization with the crystal lattice (the spin-orbit coupling). As the spin-orbit coupling is of relativistic origin, the fully-relativistic treatment to the tight-binding Korringa-Kohn-Rostoker (TB-KKR) method was introduced in the first part of this work.In the second part the in-plane magnetization of the Fe surfaces and the magnetic properties of Fe clusters were discussed and a systematicstudy comparing clusters and surface systems was performed. Fe Pt surface systems with high out-of-plane magnetic anisotropy were investigated in the third part.In the last part a detailed study of the magnetic anisotropy of thin Fe films on (001) oriented Ga As was presented. In agreement with experiment these films were found to have an in-plane anisotropy with the easy axis along the [110]-direction.In addition, the influence of Au protective layers on magnetic properties of Ga As/Fe was shown and discussed. Also, theoretical results of the spin and orbital magnetization of the Co marker in Fe film on Ga As were compared with the experimental results.