Compound systems consisting of exchange coupled ferromagnetic-antiferromagnetic multilayers are examined within the framework of the domain state model for exchange bias by means of Monte-Carlo simulations. Initially, systems with uniaxial anisotropies as well as systems where the antiferromagnet shows a twinned structure, with two easy axes then perpendicular to each other, are investigated in order to explore the reversal mechanisms during hysteresis. In both cases, a systematic variation of the angle between the field axis and one of the easy axes of the antiferromagnet reveals a rich variety of different reversal modes. For the latter one, a distinctive dependence on the direction of the cooling field is observed as well. For the characterization of the different kinds of reversal modes, the analysis of the in-plane magnetization paths of the ferromagnetic layer plays an important role. Also, the investigation of its corresponding spin structures allows for a deeper insight into the reversal mechanism. It is shown that experimentally observed asymmetries of the reversal modes in corresponding multilayer systems can be explained within the context of the domain state model. Another part of this work deals with a more general aspect of the domain state model itself, where it is shown that a bond-diluted antiferromagnet exchange coupled to a ferromagnetic layer displays the same characteristic features as the model where a site-diluted antiferromagnet is utilized. This supports the idea that it is structural disorder which is crucial for exchange bias to occur in such multilayers and the kind of disorder introduced plays only a secondary role. Finally, an outlook of nanostructured systems is given. The dependence of the exchange bias effect on the variation of the system size is investigated, where in the first setup the lateral dimension of the ferromagnet is varied, while in the second one the size of both the ferromagnet and the antiferromagnet is subject to such a variation. In both cases, a connection between the domain structure of the antiferromagnet and lateral size of the ferromagnet structure seems to be apparent. However, approaching very small systems sizes the superparamagnetic behavior demands for further investigations.