Two introductory sections describe different aspects of membranes and give a short history of membrane research. The main part of this paper is concerned with (i) the morphology of vesicles and (ii) the adhesion and interaction of membranes. [1] The morphology of vesicles can be understood in the framework of curvature models. One particularly intriguing class of shape transformations are budding or invagination phenomena. Adhesion of membranes leads to additional shape transformation and to unbinding transitions driven by thermally-excited shape fluctuations. For two interacting surfaces, one has a whole line of nontrivial transitions. Recent theoretical work indicates that such a line also governs the unbinding for bunches of more than two membranes.