We begin with a brief historical review of the development of our understanding of the normal ordering of nd orbitals of a transition metal interacting with ligands, the most common cases being three below two in an octahedral environment, two below three in tetrahedral coordination, and four below one in a square-planar environment. From the molecular orbital construction of these ligand field splittings evolves a strategy for inverting the normal order: the obvious way to achieve this is to raise the ligand levels above the metal d's; that is, make the ligands better Lewis bases. However, things are not so simple, for such metal/ligand level placement may lead to redox processes. For 18-electron octahedral complexes one can create the inverted situation, but it manifests itself in the makeup of valence orbitals (are they mainly on metal or ligands?) rather than energy. One can also see the effect, in small ways, in tetrahedral Zn(II) complexes. We construct several examples of inverted ligand field systems with a hypothetical but not unrealistic AlCH3 ligand and sketch the consequences of inversion on reactivity. Special attention is paid to the square-planar case, exemplified by [Cu(CF3)(4)](-), in which Snyder had the foresight to see a case of an inverted field, with the empty valence orbital being primarily ligand centered, the d(x2-y2) orbital heavily occupied, in what would normally be called a Cu(III) complex. For [Cu(CF3)(4)](-) we provide theoretical evidence from electron distributions, geometry of the ligands, thermochemistry of molecule formation, and the energetics of abstraction of a CF3 ligand by a base, all consistent with oxidation of the ligands in this molecule. In [Cu(CF3)(4)](-), and perhaps more complexes on the right side of the transition series than one has imagined, some ligands are sigma-noninnocent. Exploration of inverted ligand fields helps us see the continuous, borderless transition from transition metal to main group bonding. We also give voice to a friendly disagreement on oxidation states in these remarkable molecules.