We investigate a method for the controlled assembly of unilamellar vesicles consisting of bilayers assembled one leaflet at a time. We use water-in-oil emulsions stabilized by the material for the inner leaflet and produce vesicles by passing the water droplets through a second oil-water interface, where they become coated with the outer leaflet. We have used this technique to form vesicles from lipids, mixed lipid and surfactant systems, and diblock copolymers. The stability of lipid-stabilized emulsions limits the range of sizes that can be produced and the vesicle yield; nevertheless, there are several advantages with this emulsion-based technique: It is possible to make unilamellar vesicles with sizes ranging from 100 nm to 1 mum. Moreover, the process allows for efficient encapsulation and ensures that the contents of the vesicles remain isolated from the continuous aqueous phase. To illustrate possible applications of this technique, we demonstrate the use of vesicles as microreactors where we polymerize actin through the addition of magnesium and show that the polymerization kinetics are unaffected by the encapsulation.