Phase diagrams are determined by Monte Carlo lattice simulations for idealized symmetric and asymmetric surfactant molecules mixed with single-site “oil” and “water” molecules. At high concentrations (above 20%) of surfactant, the simulations show the self assembly of liquid crystalline phases, including smectic, hexagonal, BCC sphere packings, and Ia3d gyroid cubic phases. The locations of the phases on the diagram for asymmetric surfactants in “water” are shifted relative to those for a symmetric one in a way that favors phases whose surfactant-laden interfaces curve so that the bulkier group is on the convex side of the interface. When the system composition is gradually charged, cylinders of a hexagonal phase are oriented along the 111 direction of the micellar BCC or Ia3d phase into which the cylinders epitaxially transform, with the d-spacing ratios of 1.22 and 2.12, respectively. These and many other aspects of the predicted phase behavior, including the compositions at which transitions among ordered phases occur, compare favorably with experimental observations for nonionic, cationic, anionic, and zwitterionic single-tail surfactants