The anapsids are a group of amniotes, characterized by skulls without openings near the temples. The only extant members are the Testudines - turtles, tortoises, and terrapins. Various other groups, however, are known from Permian and Triassic fossils. The anapsids have traditionally been treated as a subclass of the class Reptilia, but as this group is paraphyletic they are sometimes placed in a separate class Anapsida.
Most of the anapsid orders, including the millerettids, nyctiphrurets, and pareiasaurs, were extincted in the late Permian period by the Permian-Triassic extinction event. Both the procolophonoids and some ancient ancestors of the testudines managed to survive into the Triassic, and the testidunes are the only surviving order.
External links
Introduction to Anapsida (http://www.ucmp.berkeley.edu/anapsids/anapsida.html) from UCMP
The name Parareptilia was coined by Olson 1947 to refer to an extinct group of Paleozoic reptiles, as opposed to the rest of the reptiles or Eureptilia ("true reptiles").
The name fell into disuse, until it was revived by cladistic studies, to refer to anapsida that were thought unrelated to turtles.
However this hypothesis is not very widely accepted among vertebrate paleontologists, and Benton 2000, 2004, retains the traditional class Anapsida for the "parareptiles" and turtles.