The inversion processes in substituted phosphines (R3P) and their radical cations have been investigated in detail using high-level ab initio molecular orbital and density functional theory calculations. Particular attention has been paid to the understanding of the inversion mechanism. While in PH3 and methyl derivatives only the classical vertex inversion exists, halogenated phosphines invert through C-2, T-shaped transition structures in most neutral species. The pseudo-Jahn-Teller effect in which an all circle times e＇ mixing leads a D-3h to a C-2v T-shaped transition structure is confirmed to be responsible for the edge inversion. This effect is operative upon substitution of, at least, two H atoms of PH3 by halogen atoms and appears to be largest in F-derivatives. The pseudo-JT effect is reduced in the order F > Cl > Br. Ln radical cations, the inversion barriers are consistently and substantially reduced, in such a way that in PCl3.+ and PBr3.+ the pseudo-Jahn-Teller effect virtually disappears and the edge inversion no longer exists. The effect of electron correlation on the inversion barriers has also been considered; it is small in hydrides but becomes quite large in halogenated phosphines. The ionization energies of the phosphines under consideration have also been derived.