[3] They are found in the Atlantic, the western and central Pacific, and the Gulf of California, inhabiting deep waters at or close to the sea floor.

As a result, 19th century authors generally used Galeus for the tope sharks, and Pristiurus, coined by Charles Lucien Bonaparte in 1834, for the sawtail catsharks.

Therefore, in 1908 Henry Weed Fowler designated G. melastomus as the type species of Galeus, establishing the genus to contain the sawtail catsharks.

Fowler's definition of Galeus gained widespread acceptance after Henry Bryant Bigelow and William Charles Schroeder's 1948 taxonomic review.

[8] Leonard Compagno has placed Galeus with Apristurus, Bythaelurus, Cephalurus, Parmaturus, and Pentanchus in the tribe Pentanchini of the subfamily Pentanchinae, based on morphological characters.

[9] Galeus was suggested to be the sister group of Apristurus in a 2005 phylogenetic study based on mitochondrial and nuclear DNA gene sequences, by Samuel Iglésias and colleagues.

[8] The affinity between Galeus and Apristurus was also upheld, albeit weakly, in a 2006 phylogenetic analysis based on three mitochondrial DNA genes, by Brett Human and colleagues.

A few outlying species are found in the South Atlantic (G. mincaronei and G. polli), Oceania (G. gracilis and G. priapus), and the Gulf of California (G. piperatus).

[3][10][11] Sawtail catsharks are demersal in habits and occur in deep water over outer continental and insular shelves and upper slopes.

Galeus species are typically grayish or brownish above and lighter below, and most have a pattern of darker saddles and/or blotches along the back and tail.

[10] In Suruga Bay, the dietary compositions of G. eastmani and juvenile G. nipponensis differ significantly, suggesting there is reduced interspecific competition between co-occurring Galeus species.

[16] Sawtail catsharks pose no danger to humans and have little economic value, though varying numbers are caught incidentally by deepwater commercial fisheries.