Keywords: Wetting phenomena, surface domains, surface topography, contact line pinning, fluid membranes, vesicles, intrinsic contact angles Abstract: Two types of wetting phenomena will be discussed: (i) Morphological wetting transitions at chemically patterned or topographically structured substrates; and (ii) Wetting of flexible membranes such as lipid bilayers by aqueous phases. Morphological wetting transitions between different droplet shapes occur, e.g., as one varies the amount of liquid deposited on the structured substrate. [1,2] The basic mechanism underlying this polymorphism is the freedom of contact angles at pinned contact lines. [3] The second system consists of lipid vesicles containing aqueous solutions with two species of water-soluble polymers. When the polymer concentrations are raised by deflation, the aqueous solution forms two coexisting liquid phases that may undergo complete-to-partial wetting transitions at the vesicle membranes. [4] Partial wetting is characterized by effective contact angles that can be measured by optical microscopy and by an intrinsic contact angle that represents a 'hidden' material parameter. [5] [1] R. Seemann et al. PNAS 102, 1848 (2005) [2] P. Blecua, M. Brinkmann, R. Lipowsky, and J. Kierfeld. Langmuir (in press) [3] R. Lipowsky et al. J. Phys.: Condens. Matter 17, S2885 (2005) [4] Y.-H. Li, R. Lipowsky, and R. Dimova. JACS 130, 12252 (2008) [5] H. Kusumaatmaja, Y.-H. Li, R. Dimova, and R. Lipowsky. Phys. Rev. Lett. (submitted)