The AMO3 perovskites containing transition-metal atoms M have an MO3 array with M-O-M bond angles 180°-φ in which the angle φ increases with the mismatch of the A-O and M-O equilibrium bond lengths. The tight-binding bandwidths for the π-bonding t and σ-bonding e orbitals of d-orbital parentage are Wπ < Wσ. In the orthomanganites Ln1−xAxMnO3 with A an alkaline earth, the octahedral-site high-spin Mn3+ ions have a d-electron configuration t3e1:5Eg that is orbitally twofold-degenerate, and the on-site electron-electron coulomb energy for adding a fifth d electron is Uσ ≈Wσ > Wπ. Consequently the equilibrium reaction t3e1 ≈ t3 σ*1 for a first-order transition from localized-e to itinerant-σ* electrons is shifted to the left as the bandwidth Wσ ≈ 12 εσλσ 2 cos φ is narrowed by increasing φ, by perturbations of the periodic potential of the MO3 array, and/or by increasing spin-disorder scattering; it is shifted to the right by oxidation of the MnO3 array, by application of a magnetic field, and by pressure. Cross-over from polaronic-e to itinerant-σ* electrons at a ferromagnetic Curie temperature Tc or a charge-ordering temperature Tco < Tc can give a “colossal” negative magnetoresistance provided the Fermi energy εF lies below a mobility edge μc in the narrow σ* band of the ferromagnetic phase. Cooperative Jahn-Teller distortions that remove the orbital degeneracy of a localized 5Eg configuration also introduce unusual antiferromagnetic ordering of the manganese-atom spins.