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A simple model for the adhesion of vesicles to interfaces and membranes is introduced and theoretically studied. It is shown that adhering (or bound) vesicles can exhibit a large variety of different shapes. The notion of a contact angle governed by tension is found to be applicable only for a restricted subset of these shapes. Furthermore, the vesicle undergoes a nontrivial adhesion transition from a free to a bound state. This transition is governed by the balance between the overall bending and adhesion energies, and occurs even in the absence of shape fluctuations.