The field of metallosupramolecular chemistry has advanced rapidly in recent years. Much work in this area has focused on the formation of hollow self-assembled metal-organic architectures and exploration of the applications of their confined nanospaces. These discrete, soluble structures incorporate metal ions as 'glue' to link organic ligands together into polyhedra.Most of the architectures employed thus far have been highly symmetrical, as these have been the easiest to prepare. Such high-symmetry structures contain pseudospherical cavities, and so typically bind roughly spherical guests. Biomolecules and high-value synthetic compounds are rarely isotropic, highly-symmetrical species. To bind, sense, separate, and transform such substrates, new, lower-symmetry, metal-organic cages are needed. Herein we summarize recent approaches, which taken together form the first draft of a handbook for the design of higher-complexity, lower-symmetry, self-assembled metal-organic architectures.