by Greg Mayer (Update below)
Lizards are far and away the most species-rich group of living reptiles, with over 7000 species. One of the first things you learn if you’re a little boy interested in such creatures is that snakes are lizards. One of the other things you learn is that snakes are not the only group of legless lizards. There are, in fact, many groups of lizards with reduced or missing legs, such as the European slow worm and American glass snakes (now preferably called glass lizards). Snakes are just the most evolutionarily successful such group of lizards, comprising 3000 or so of the species of lizards. One of the most distinctive of the non-snake legless lizards are the worm lizards, or amphisbaenians, a group of about 150, mostly tropical, burrowing species. Perhaps our greatest student of the group, the late Carl Gans, thought them so distinctive that he championed a classification in which they were ranked equally with lizards and snakes within the Squamata (the taxon which includes lizards and all their derivatives, including snakes and amphisbaenians), although most other workers did not accept this ranking.

Gans wrote in his Biomechanics (he was a functional morphologist and physiologist as well as a systematist) that:
Unfortunately, we lack fossils intermediate between the Amphisbaenia and other groups, and can only speculate what their ancestors looked like.

Ever since Charles L. Camp’s 1923 classic, “Classification of the lizards”, amphisbaenians have bounced around a bit in terms of who their closest relatives are (this proposal being the most heterodox), but recent molecular work (summarized here and here by Blair Hedges and Nicolas Vidal) has connected them to the Lacertidae, a group of typical-looking Old World lizards (‘lacerta’ is Latin for ‘lizard’). In describing the new species, known from a single, well-preserved, and nearly complete specimen, Muller and colleagues write that the species shows “a mosaic of lacertid and amphisbaenian anatomical characters”. The skull, like that of amphisbaenians, is strongly constructed, and evidently adapted for a semi-fossorial life, while the limbs, though well developed proximally, are fairly short and have miniaturized digits. The body is not elongated. Morphometric comparison to modern lizards show that Cryptolacerta was likely a cryptic, leaf litter dwelling form.
Thus, the burrowing head evolved before the fully fossorial life style, while the body was as yet unenlongated, and the limbs still fairly well developed. We should not be surprised to find limbs in a transitional form from the well-limbed lacertids, but it is also the case that three extant species of worm lizards, the members of the Mexican genus Bipes, retain short front legs. Though very short, the limbs are well-developed for mole-like burrowing.

The New York Times has a story on this, which gets the gist of the story right, but the headline (“Fossil Sheds Light on the Lizard-Snake Divide”) and lede (“The origin of snakes is a perplexing matter”) are way off: the paper concerns the origin of amphisbaenians, not snakes.
h/t: Matthew Cobb
UPDATE: Burrowing lizards seem to be all the rage this week, as alert readers Dominic and James C. Trager have pointed out two other burrowing lizard events in the comments below. First, a new species of blind skink, Dibamus, has been described by Thy Neang and colleagues in the journal Zootaxa (BBC piece here). There are about ten species of dibamids, which lack forelimbs, but have flap-like hindlimbs. Like amphisbaenians, they have bounced around a bit in their classification; the latest work (see papers by Hedges and Vidal below) places them as the earliest branch within the lizards. I’m not sure why this new species merited news coverage, except insofar as all new species are newsworthy. One of the authors of the new species is Lee Grismer, whose alpha taxonomic exploits we’ve noted here at WEIT before.
The second item is a paper by Steve McAlpin and colleagues at Macquarie University in Plosone, describing heretofore unknown complexity in lizard social behavior (NY Times piece here). I’ll let the abstract speak for itself:
Here we provide the first example of a lizard that constructs a long-term home for family members, and a rare case of lizards behaving cooperatively. The great desert skink, Liopholis kintorei from Central Australia, constructs an elaborate multi-tunnelled burrow that can be continuously occupied for up to 7 years. Multiple generations participate in construction and maintenance of burrows. Parental assignments based on DNA analysis show that immature individuals within the same burrow were mostly full siblings, even when several age cohorts were present. Parents were always captured at burrows containing their offspring, and females were only detected breeding with the same male both within- and across seasons. Consequently, the individual investments made to construct or maintain a burrow system benefit their own offspring, or siblings, over several breeding seasons.
Complex social behavior is well known in crocodilians and, of course, birds (which are glorified reptiles), but this is a unique case for squamates (so far). They don’t seem to be eusocial though, which, in addition to overlapping generations, requires cooperative care of the young (there is at least some indirect parental care here), and a reproductive division of labor. The skinks involved are burrowing, but well-limbed.

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Camp, C.L. 1923. Classification of the lizards. Bulletin of the American Museum of Natural History 48:289-481. (pdf)
Hedges, S. B. and N. Vidal. 2009. Lizards, snakes, and amphisbaenians (Squamata). Pp. 383-389 in S. B. Hedges and S. Kumar, eds., The Timetree of Life, Oxford University Press, New York. (pdf)
McAlpin, S., P. Duckett and A. Stow. 2011. Lizards cooperatively tunnel to construct a long-term home for family members. Plosone 6(5):e19041, 4pp. (pdf link)
Muller J., C.A. Hipsley, J.J. Head, N. Kardjilov, A. Hilger, M.Wuttke and R.R. Reisz. 2011 Eocene lizard from Germany reveals amphisbaenian origins. Nature 473:364-367. (abstract)
Neang, T., J. Holden, T. Eastoe, R. Seng, S. Ith, and L.L. Grismer. 2011. A new species of Dibamus (Squamata: Dibamidae) from Phnom Samkos Wildlife Sanctuary, southwestern Cardamom Mountains, Cambodia. Zootaxa 2828:58-68. (abstract)
Vidal, N. and S. B. Hedges. 2009. The molecular evolutionary tree of lizards, snakes, and amphisbaenians. Compte Rendus Biologies 332:129-139. (pdf)