Abstract: Recent experiments on vesicles formed from block copolymers with liquid-crystalline side-chains reveal a rich variety of vesicle morphologies. The additional internal order (\structure") developed by these self-assembled block copolymer vesicles can lead to signicantly deformed vesicles as a result of the delicate interplay between two-dimensional ordering and vesicle shape. The inevitable topological defects in structured vesicles of spherical topology also play an essential role in controlling the final vesicle morphology. Here we develop a minimal theoretical model for the morphology of the membrane structure with internal nematic/smectic order. Using both analytic and numerical approaches, we show that the possible low free energy morphologies include nano-size cylindrical micelles (nano-fibers), faceted tetrahedral vesicles, and ellipsoidal vesicles, as well as cylindrical vesicles. The tetrahedral vesicle is a particularly fascinating example of a faceted liquid-crystalline membrane. Faceted liquid vesicles may lead to the design of supra-molecular structures with tetrahedral symmetry and new classes of nano-carriers.