Novel materials and advances in surgery lead to an increasing application of biomaterials within the human body e.g. after trauma or to regain normal human body functions. The achievement of an integration of these biomaterials into the human tissue via the attachment of somatic cells is one of the most important goals of biomaterial science. Especially, biomaterial-associated inflammations, thrombosis and infections that are triggered by the attachment of proteins and bacteria to the biomaterial surface and lead often to a perturbation of this integration process. In this thesis the attachment processes of proteins and bacteria to biomaterial surfaces is theoretically investigated. New aspects of the surface influence on the attachment process become accessible with the application of the here introduced novel models: A multiscale finite difference/cellular automaton model of the adsorption of the blood plasma protein fibrinogen is used to simulate the kinetics and its arrangement on the surface. The results give insight into the role of several surface parameters on the dynamics of protein adsorption and protein network formation. In addition a novel 3-D model is used to investigate the interaction of spherical bacteria with biomaterial surfaces of arbitrary shape. It is based on fundamental concepts of colloid chemistry applying full 3-D calculation of interfacial forces in aqueous media with a realistic surface topography. The calculations are the first proof that standardized roughness parameters based on an amplitude description of the surface topography are insufficient for the description of the impact on bacterial adhesion. Summarizing, this thesis gives a close-to-reality description of the influence of biomaterial interfaces on the attachment processes of proteins and bacteria as an important step on the road to the design of tailored biomaterial surfaces.