Under certain circumstances, metal complexes with a formal d0 electronic configuration may exhibit structures that violate the traditional structure models, such as the VSEPR concept or simple ionic pictures. Some examples of such behavior, such as the bent gas-phase structures of some alkaline earth dihalides, or the trigonal prismatic coordination of some early transition metal chalcogenides or pnictides, have been known for a long time. However, the number of molecular examples for “non-VSEPR” structures has increased dramatically during the past decade, in particular in the realm of organometallic chemistry. At the same time, various theoretical models have been discussed, sometimes controversially, to explain the observed, unusual structures. Many d0 systems are important in homogeneous and heterogeneous catalysis, biocatalysis (e.g. molybdenum or tungsten enzymes), or materials science (e.g. ferroelectric perovskites or zirconia). Moreover, their electronic structure without formally nonbonding d orbitals makes them unique starting points for a general understanding of structure, bonding, and reactivity of transition metal compounds. Here we attempt to provide a comprehensive view, both of the types of deviations of d0 and related complexes from regular coordination arrangements, and of the theoretical framework that allows their rationalization. Many computational and experimental examples are provided, with an emphasis on homoleptic mononuclear complexes. Then the factors that control the structures are discussed in detail. They are a) metal d orbital participation in σ bonding, b) polarization of the outermost core shells, c) ligand repulsion, and d) π bonding. Suggestions are made as to which of the factors are the dominant ones in certain situations. In heteroleptic complexes, the competition of σ and π bonding of the various ligands controls the structures in a complicated fashion. Some guidelines are provided that should help to better understand the interrelations. Bent's rule is of only very limited use in these types of systems, because of the paramount influence of π bonding. Finally, computed and measured structures of multinuclear complexes are discussed, including possible consequences for the properties of bulk solids.