I have read that once it was thought that monitor lizards were more closely related to snakes than to other lizards. Apparently, that’s recently been reconsidered, although not everyone has accepted it (or they’re just slow in getting things updated).
Anyway. . .
Not being an expert, I’ll buy that the more recent research indicates monitors are actually more closely related to most other lizards (don’t know whether that includes iguanas or tuataras, though).
But what was the reasoning behind the thinking that snakes were their next of kin?
Much of that thinking came from a pair of papers: “Squamate phylogeny and the relationships of snakes and mosasaurids” (Caldwell, M., 1999) and “The phylogeny of varanoid lizards and the affinties of snakes” (Lee, M., 1997). Primarily, these presumed affinities centered around similarities in dentition, braincase structure and the make-up of the intramandibular joint. I’m not familiar with the details, but those two papers (as well as others by Lee and/or Caldwell from 1997 through about 2004) should explain the specifics of those similarities.