It contains only a single living genus Squatina, commonly known as angelsharks.

The oldest genus of the order, Pseudorhina is known from the Late Jurassic of Europe.

[1] Three other genera, Cretasquatina, Cretascyllium and Parasquatina are known from Cretaceous fossils from North America and Europe,[2][3] though the placement of Parasquatina in the order has been questioned.

[1] All living and extinct members of the order share a similar body morphology[2] with a highly flattened body with enlarged pectoral and pelvic fins suggestive of a bottom-dwelling ambush predator ecology.

[2] The earliest records that can be assigned with confidence to the modern genus are known from the Early Cretaceous (Aptian) of England.