The lollipop catshark was originally described by American ichthyologist Charles Henry Gilbert as Catulus cephalus, in the 1892 14th volume of Proceedings of the United States National Museum.

[3] Based on morphological and molecular phylogenetic evidence, Cephalurus is thought to form a clade with the genera Asymbolus, Parmaturus, Galeus, and Apristurus.

[3] The lollipop catshark is so named because of its peculiar tadpole-like shape, with an enormously expanded head and branchial region (containing the gills) coupled with a slender, cylindrical body tapering towards the tail.

The snout is very short and blunt, with widely spaced nostrils flanked by moderately developed flaps of skin.

The pectoral fins are angular, twice as long as wide, and originate beneath the fourth gill slit.

[4] The coloration is a plain brownish gray all over, sometimes lightening to almost white at the dorsal, pectoral, and pelvic fin margins.

[9] The lollipop catshark is aplacental viviparous, with birthing apparently taking place in early summer.

Females have two functional ovaries and retain pairs of thin-shelled egg cases (one within each oviduct) within their bodies until they hatch.