Block copolymers constitute a class of self-assembling macromolecules that offer remarkable flexibility for controlling nanostructure, both in discrete objects and in bulk materials. Block copolymer micelles may be formed with multiple compartments by judicious choice of ingredients in an ABC triblock copolymer. For example, we have shown that a poly(ethylene oxide–b–styrene–b–fluorinated butadiene) triblock assembles in dilute aqueous solution into large, flat core/shell/corona disks, with the fluorine containing block forming the core. In contrast, the unfluorinated precursor generates large spherical micelles. A numerical analysis suggests that the disk-like motif is characteristic of the so-called superstrong segregation regime, whereby the interfacial tension becomes so large as to overwhelm the conformational entropy of the core blocks. For ABC miktoarm stars comprising polyethylene oxide, polyethylethylene, and polyhexafluoropropylene oxide arms, a much richer variety of micellar structures are observed. Prominent amongst these is a “segmented worm”, in which alternating layers (5–7 nm thick) of hydrocarbon and fluorocarbon blocks form disks (6–10 nm in radius) that stack into cylindrical aggregates. The disk radii suggest almost fully stretched blocks, again consistent with the superstrong segregation regime. These structures are rationalized in terms of the constraints imposed by the star architecture, combined with the extremely strong interfacial tensions. In contrast, for lipids, surfactants, and aqueous diblock copolymers, increasing the interfacial tension can induce a transition from spheres to cylinders to flat bilayers; the disk-like motif is not usually seen. Interestingly, in aqueous diblocks both worm-like micelles and vesicles have been well-documented, whereas in “simple” organic systems they have not. We have shown that by suitable choice of block composition and solvent selectivity, the curvature sequence sphere/cylinder/vesicle can also be observed in poly(styrene–b–isoprene) diblocks in dialkyl phthalates. In more concentrated solutions such spherical micelles assemble onto body-centered or face-centered cubic lattices. In some cases a thermoreversible fcc/bcc transition has been noted. We have recently demonstrated that this transition corresponds to a particular aggregation number; higher aggregation numbers, found at lower temperatures, favor the “hard-sphere-like” fcc packing. All of these results are based on a combination of dynamic light scattering, small angle X-ray and neutron scattering, and cryogenic transmission electron microscopy.