The chapter deals with the physical properties of model membranes composed of lipid–protein mixtures. Lateral phase separation of lipids and proteins associated with lipid phase transitions and selective lipid–protein interactions which may control the lateral organization of these membranes are also discussed. The bilayer contained in biomembranes represents a multicomponent mixture of lipids and proteins. A central question of membrane biophysics is whether lipids play an active role for the self assembly and function of biomembranes. The chapter describes the structural dynamics and elastic properties of fluid and solid bilayer vesicles together with the thermodynamics of the thermotropic phase transitions. It focuses on the advantage of lipid bilayers as two-dimensional solvent and the physics of lipid mixtures is discussed on a thermodynamic basis. Even more important is to show that lipid bilayers are exciting as model systems to explore the novel and rich physical properties of soft two-dimensional materials.