Experiments on LaCoO3 demonstrate that crystal-field theory and band theory describe two thermodynamically different electronic phases. For an integral number of electrons per atom, the phase transition is first-order. The critical parameter is an overlap integral, which may be either a cation-cation or a cation-anion-cation overlap integral. Intra-atomic exchange and electron-phonon interactions contribute significantly to electron localization. The characteristic feature of collective electrons is a Fermi surface. Those physical properties that depend upon the existence of a Fermi surface vary discontinuously through a localized-electron ⇄ collective-electron transition; other physical properties, including electron mobility and paramagnetic susceptibility, apparently do not. It is argued that the spontaneous crystallographic distortions associated with semiconducting ⇄ metallic phase changes manifest the existence of narrow, cation-sublattice bands if the cations are removed from the centers of symmetry of their interstices, narrow crystalline bands otherwise; ferroelectric and antiferroelectric transitions manifest the existence of a narrow valence band; the formation of a homologous series of shear structures in nonstoichiometric compounds manifests narrow conduction bands. These distortions all result from the creation, or enhancement, of an energy discontinuity at the Fermi surface. By contrast, conventional Jahn-Teller distortions, magnetostriction due to spin-orbit coupling, and the ordering of small polarons manifest localized electrons and the applicability of crystal-field theory. It is also shown that the critical overlap integral (or bandwidth) for spontaneous band magnetism is only a little larger than that for a localized-electron ⇄ collective-electron transition. Preliminary data are compatible with two possibilities for bands that are more than half-filled: (1) saturation of orbitals ofα spin, which leads to localized electrons ofα spin and collective electrons ofβ spin; (2) spontaneous magnetization (ferromagnetism) of only the antibonding electrons, which may lead to reduced atomic moments. Spontaneous band antiferromagnetism may be stabilized in bands that are half-filled or slightly less. It is represented by a spin-density wave with wavelength adjusted to create an energy discontinuity at the Fermi surface. Spin-density waves are also possible among collectiveβ-spin electrons that are coupled to localizedα-spin electrons.