AbstractThe diversity of phase morphologies observed recently in star-branched liquid-crystalline and polymeric compounds containing at least three immiscible segments is reviewed. Bolaamphiphiles and facial amphiphiles with rodlike aromatic cores, two end-groups, and one (T-shape) or two (X-shape) chains attached laterally to the core, form numerous honeycomblike liquid-crystal phases, as well as a variety of novel lamellar and 3D-ordered mesophases. Molecular self-organization is described in bulk phases and in thin films on solid and liquid surfaces, as well as in Langmuir–Blodgett films. The remarkably reversible formation of mono- and trilayer films is highlighted. In the bulk, T-shaped “rod–coil” molecules without appended end-groups form predominantly lamellar phases if the core is a straight rod, but the bent-core variety forms hexagonal honeycombs. Furthermore, self-assembly of “Janus”-type molecules, is discussed. Also covered is the diversity of morphologies observed in miktoarm star terpolymers, i.e., polymers with three different and incompatible arms of well defined lengths. Similarities and differences are highlighted between the liquid-crystal morphologies on the 3–15 nm scale and the polymer morphologies on the scale of 10–100 nm. A separate section is dedicated to computer simulations of such systems, particularly those using dissipative particle and molecular dynamics. Of special interest are the recently synthesised X-shaped tetraphilic molecules, where two different and incompatible side-chains are attached at opposite sides of the rodlike core. The tendency for their phase separation produces liquid-crystal honeycombs with cells of different compositions that can be represented as a plane paved with different colored tiles. The independent variation of chain length and “color” creates the potential for developing a considerable range of complex new 2D and 3D soft nanostructures. Analogous X-shaped rod–coil compounds with unequal side groups are also of considerable interest, forming tubular lyotropic structures capable of confining strings of guest molecules.