Supported lipid bilayers (SLBs) have been a standard model system for experimental investigations of biomembranes. The difference between supported and unsupported membranes which is crucial for the applicability of these models has, however, not been studied very systematically. In simulations this is even more true as computational studies of supported lipid bilayers are essentially lacking from the literature. We are aiming at filling this gap by a multiscale approach to address the influences various types of supports have on the structure, dynamics and phase behavior of lipid bilayers. We are using various molecular models on different time and length scales in order to address the multitude of effects. Our simulations demonstrate that these simulation models can predict different aspects of the change of the system under the influences of hydrophilic and hydrophobic support. It becomes very clear that the support breaks the symmetry of the membrane and suppresses large amplitude fluctuations. The structural influence on the proximal leaflet is much more strongly pronounced than for the distal leaflet. It turns out that the distal leaflet is a reasonable model for a leaflet in a free bilayer but the proximal leaflet is strongly coupled to the support. We also find that the lateral pressure profile close to the support is strongly changed and this may provide clues why proteins in supported lipid bilayers can loose their function.