The genus was named in 1971 by Aleksandr Grigorevich Sharov. The type species is Sordes pilosus. The genus name means "filth" or "scum" in Latin, a reference to evil spirits in local folklore. The specific name is Latin for "hairy"; despite sordes being feminine, it has not yet been emended to pilosa.
Sordes had a 0.63 m (2 ft) wingspan. The wings were relatively short. It had a slender, not round, head with moderately long, pointed jaws. The skull was about 8 cm (3.2 in) long. Its teeth were widely spaced, small and slanted. It had a short neck. It had a long tail, accounting for over half its length, with at the end an elongated vane. Unlike many pterosaurs, it had no head crest. Sordes had, according to Sharov and Unwin, wing membranes attached to the legs and a membrane between the legs. Sordes probably ate small prey, perhaps including insects and amphibians.
Sordes has been assigned to the family Rhamphorhynchidae. These were among the earliest of the pterosaurs, evolving in the late Triassic and surviving to the late Jurassic. According to Unwin, within Rhamphorhynchidae Sordes belonged to the Scaphognathinae. Other researchers however, such as Alexander Kellner and Lü Junchang, have produced cladistic analyses showing that Sordes was much more basal, and not a rhamphorhynchid.
The genus is based on holotype PIN 2585/3, a crushed relatively complete skeleton on a slab. It was found in the sixties at the foothills of the Karatau in Kazakhstan. The fossil shows remains of the soft parts, such as membranes and hair-like filaments. This was the first unequivocal proof that pterosaurs had a layer of hair-like filaments covering their bodies, later named pycnofibres. The pycnofibres served as insulation, an indication the group was warm-blooded, and provided a streamlined flight profile. The pycnofibres are present in two main types: longer at the extreme part of the wing membrane and shorter near the body. In the 1990s, David Unwin argued that both types were essentially not hairs but reinforcing fibres of the flight membranes. Later he emphasized that "hair" in the form of pycnofibres was indeed present on the body, after the find of new specimens clearly showing this.
Sharov had already referred a paratype or second specimen: PIN 2470/1, again a fairly complete skeleton on a slab. By 2003 another six specimens had been discovered.