Vesicles are compartments enclosed by a thin membrane, which is made up of amphiphilic molecules arranged into ordered layers. Vesicle-like structures are Nature's choice for encapsulating important biochemical species that enable living processes, and are increasingly important as artificial structures for the encapsulation and release of drugs, biomolecules and other active ingredients for biomedical, pharmaceutical, food and consumer industries. Advances in microfluidic technologies have provided a new set of tools for unraveling the science behind formation of vesicles and fabricating novel vesicles. While traditional approaches for fabricating vesicles rely on self-assembly of amphiphiles, the precise control of flow afforded in microfluidic devices enables directed assembly of the amphiphiles. Thus, techniques such as hydrodynamic flow focusing, controlled emulsion-templating and pulsatile jetting offer unprecedented degree of control over vesicle structures. This creates new opportunities to engineer the structures of vesicles and tailor them for specific applications. In this review, we introduce current understanding behind different kinds of vesicles, survey conventional and microfluidic techniques for their formation, discuss new approaches of encapsulation and release of active ingredients in microfluidic vesicles, and point to future research and development in the area.