Supported and Tethered Lipid Bilayers are an abundant research platform for understanding the behavior of cell membranes as they allow for additional mechanical stability and enable characterization techniques not reachable otherwise. We present systematic studies on different length scales of the changes that a support inflicts on a phospholipid bilayer using molecular modeling. We characterize the density and pressure profiles as well as the density imbalance induced by the support. It turns out that the changes in pressure profile are strong enough that protein function should be impacted leading to a previously neglected mechanism of transmembrane protein malfunction in supported bilayers. We determine the diffusion coefficients and characterize the influence of corrugation of the support. We also measure the free energy of transfer of phospholipids between leaflets using the coarse-grained Martini model. It turns out that there is at equilibrium about a 2-3% higher density in the proximal leaflet. These results are in agreement with data obtained by very large scale modeling using a water free model where flip-flop can be observed directly. We are additionally presenting recent results on tethered bilayers which are chemically bound to the support.