The interactions between membranes and polymers can have rather dramatic effects as recently observed for lipid vesicles in aqueous solutions of two water-soluble polymers, dextran and polyethylene glycol (PEG). Deflation of the vesicles leads to aqueous phase separation within the interior compartments, and the membranes become exposed to several aqueous phases. The overall morphology of the vesicles is then determined by the wetting properties of the membranes. These properties can be characterized by an intrinsic contact angle [6], which represents a material parameter and can be calculated from the effective contact angles as measured by optical microscopy. As one changes the polymer concentration, the system may undergo a complete-to-partial wetting transition [7]. In addition, deflation-induced phase separation leads to the formation of a large number of stable membrane nanotubes [8], which reveal spontaneous membrane tensions [9].