The debate over the nature and classification of hypervalent molecules goes back to Gilbert N. Lewis and Irving Langmuir and the debate over the nature of the chemical bond in the 1920s.  Lewis maintained the importance of the two-center two-electron (2c-2e) bond in describing hypervalence, thus using expanded octets to account for such molecules.  Using the language of orbital hybridization, the bonds of molecules like PF and SF were said to be constructed from spd orbitals on the central atom.  Langmuir, on the other hand, upheld the dominance of the octet rule and preferred the use of ionic bonds to account for hypervalence without violating the rule (e.g. " 2F" for SF).
In the late 1920s and 1930s, Sugden argued for the existence of a two-center one-electron (2c-1e) bond and thus rationalized bonding in hypervalent molecules without the need for expanded octets or ionic bond character; this was poorly accepted at the time.  In the 1940s and 1950s, Rundle and Pimentel popularized the idea of the three-center four-electron bond, which is essentially the same concept which Sugden attempted to advance decades earlier; the three-center four-electron bond can be alternatively viewed as consisting of two collinear two-center one-electron bonds, with the remaining two nonbonding electrons localized to the ligands.
The attempt to actually prepare hypervalent organic molecules began with Hermann Staudinger and Georg Wittig in the first half of the twentieth century, who sought to challenge the extant valence theory and successfully prepare nitrogen and phosphorus-centered hypervalent molecules. The theoretical basis for hypervalency was not delineated until J.I. Musher's work in 1969.
In 1990, Magnusson published a seminal work definitively excluding the significance of d-orbital hybridization in the bonding of hypervalent compounds of second-row elements.  This had long been a point of contention and confusion in describing these molecules using molecular orbital theory. Part of the confusion here originates from the fact that one must include d-functions in the basis sets used to describe these compounds (or else unreasonably high energies and distorted geometries result), and the contribution of the d-function to the molecular wavefunction is large.  These facts were historically interpreted to mean that d-orbitals must be involved in bonding.  However, Magnusson concludes in his work that d-orbital involvement is not implicated in hypervalency.
Nevertheless, a 2013 study showed that although the Pimentel ionic model best accounts for the bonding of hypervalent species, the energetic contribution of an expanded octet structure is also not null.  In this modern valence bond theory study of the bonding of xenon difluoride, it was found that ionic structures account for about 81% of the overall wavefunction, of which 70% arises from ionic structures employing only the p orbital on xenon while 11% arises from ionic structures employing an hybrid on xenon. The contribution of a formally hypervalent structure employing an orbital of spd hybridization on xenon accounts for 11% of the wavefunction, with a diradical contribution making up the remaining 8%. The 11% spd contribution results in a net stabilization of the molecule by  mol, a minor but significant fraction of the total energy of the total bond energy ( mol).  Other studies have similarly found minor but non-negligible energetic contributions from expanded octet structures in SF (17%) and XeF (14%).
Despite the lack of chemical realism, the IUPAC recommends the drawing of expanded octet structures for functional groups like sulfones and phosphoranes, in order to avoid the drawing of a large number of formal charges or partial single bonds.