Previously, I'd used the papers by Griffiths (1999) and Griffiths et al. Accordingly, the White-rumped Falcon is placed in the monotypic genus Neohierax (Swann, 1922).
Falco itself seems to have originated much more recently, with a common ancestor most likely between 5 and 8 million years ago, a good reason to leave all of Falco in a single genus.
The seriemas have sometimes been considered Gruiformes, but genetic evidence points elsewhere. Besides the Cariamidae, the Cariamae are thought to have included three now-extinct families: the Phorusrhacidae (S. See Alvarenga and Höfling (2003) for more on the Phorusrhacidae. This is interesting as the crown-groups of their sister taxa (Psittaciformes plus Passeriformes) are older, much older.
The phylogeny is now based on the multigene analysis of Fuchs et al. If the falcons are correctly placed as sister to the parrots and passeriformes, they must have originated in the early part of the Eocene or more likely Paleocene, perhaps 50-60 million years ago (some estimates make them even older).
This remains true even after Fuchs et al.'s (2015) analysis. I had earlier used the name Nestoridae, which seemed to be the most common usage for a family containing both Strigops and Nestor.
The order of Falco itself is now based on Fuchs et al. However, both family-group names were introduced at the same time (Bonaparte, 1849), and they have normally been kept separated enough that the issue of priority doesn't arise.
The African kestrel clade was studied by Groombridge et al. Based on their work, Rock Kestrel must be split from Eurasian Kestrel because the Australian Kestrel is split. (2006) gives a nice overview of the Arini, with Kirchman et al. Russello and Amato found that the for last four (possibly five) Amazona species, the genetic data does not seem to match existing subspecies.
The Hierofalco complex was examined in detail by Wink et al. In spite of sampling many individuals, they were unable to produce a clean phylogeny. Christidis and Boles (2008) contains detailed information on Australian parrots. (2011) provided further information concerning the Cockatoos; Groombridge et al. (2012) were helpful with the Psittaculini; the placement of the Ground and Night Parrots is inspired by Leeton et al. Although crown group parrots appear to originate in the Australo-Pacific region, there is plenty of fossil evidence that the early parrots were much more widespread.
I can't find an alternate name for the Amazonian ochrocephala, so I've labelled them as ochrocephala (Amazon) and ochrocephala (Orinoco).
The literature refers to a Central (meaning Middle) American clade, Northern South American (NSA) clade and two South American clades (SA1 and SA2).
There's a slight plumage difference, but it doesn't seem strong enough to provide a separating mechanism. There is substantial variation in the Yellow-headed Amazon complex.