This critical review focuses on recent progress in the field of T-shaped ternary amphiphiles. These molecules can self-assemble into a series of new liquid crystalline (LC) phases with polygonal cylinder structures, new lamellar phases and LC phases combining columns and layers. These structures are analyzed on the basis of symmetry, net topology and tiling pattern (Laves and Archimedean tilings) and discussed in relation to morphologies of multiblock copolymers, self organized DNA super-lattices, metal-organic frameworks, crystal-engineering and self-assembled periodic superstructures on surfaces (210 references).