Helicoprion is an extinct genus of large shark-like cartilaginous fish that lived from the Early to the Middle Permian, about 290-270 million years ago. Helicoprion is a member of the Eugeneodontiformes, an extinct order of cartilaginous fish within the clade Holocephali, a group today represented only by chimaeras. It is also the type genus of the Helicoprionidae, a family of eugeneodonts characterised by distinctive tooth structures called tooth whorls. Helicoprion was first named in 1899 by Alexander Karpinsky on the basis of fossils discovered in Russia and Australia, the generic name meaning "spiral saw". Although numerous species were subsequently assigned to the genus, only H. bessonowi, H. davisii, and H. ergassaminon are recognized following a 2013 revision. The three species are distinguished by the shape and spacing of their tooth crowns.

Helicoprion is mainly known from its fused, spiral-shaped tooth whorls, which account for almost all documented fossils of the taxon. The position and function of these structures was long debated, but studies based on specimens preserving jaw cartilage indicate that they were positioned in the lower jaw and were specialised for grasping and slicing soft-bodied prey such as cephalopods. The whorl may also have aided in shelling or extracting the bodies of nautiloids and ammonoids. Based on the skeletal anatomy of smaller eugeneodonts, Helicoprion is estimated to have reached lengths between 5 and 12 m (16 and 39 ft), with a general external appearance possibly comparable to that of tunas, swordfish, or mackerel sharks. Fossils of Helicoprion are known from marine deposits worldwide, indicating that it was pelagic and had a cosmopolitan distribution. The highest concentrations of these come from Idaho and Russia, which used to be covered by depp inland seas where Helicoprion may have congregated.

The first known specimen of Helicoprion consists of a partial tooth whorl preserving 15 teeth, 14 of which are visible. It was discovered in Western Australia in a tributary of the Gascoyne River by a gold prospector named Mr. Davis, his first name being unknown. Now housed in the Western Australian Museum under the catalogue WAMAG 9080, the fossil was not found in situ, thus its precise stratigraphic origin remains uncertain. In 1884, Irish meteorologist Robert Henry Scott forwarded to British paleontologist Henry Woodward a letter written by a reverend from Fremantle, accompanied by a photograph of the find. Because of its incomplete condition, Woodward identified the fossil as being very similar to those of the cartilaginous fish Edestus, a genus first described by American paleontologist Joseph Leidy in 1855. Wishing to examine the fossil directly, Woodward persuaded Scott to write to his sister, Lady Barker, to obtain the loan of the specimen from the same reverend. After an extended correspondence, Irish geologist Edward Hardman, then on assignment in the Kimberley region, was tasked with bringing the fossil back to England upon his return. In a 1886 publication, Woodward finally described the specimen as representing a new species of Edestus, which he named Edestus davisii in honor of its discoverer.

More complete tooth whorls were discovered in the late 19th century by Alexander G. Bessonov of the Russian Academy of Sciences, in a quarry near the town of Krasnoufimsk in Sverdlovsk Oblast. He sent them to geologist Alexander Karpinsky, who first described them in a monograph published in Russian in 1899, followed later that year by a German translation. As the fossils he examined were sufficiently distinct from those of Edestus, Karpinsky assigned them to a new genus, which he named Helicoprion, with H. bessonowi as the type species. The generic name Helicoprion derives from the Ancient Greek ἕλικος (hélikos, "spiral") and πρίων (príōn, "saw"), in reference to the characteristic morphology of the tooth whorls, while the specific epithet bessonowi honors their discoverer. Among the six specimens described by Karpinsky, the most complete of them, later catalogued as TsNIGR 1/1865 in the collections of the Central Research Geological Museum [ru] in Saint Petersburg, was designated as the lectotype by Russian paleontologist Dmitry Obruchev [ru] in a 1964 publication. This same specimen was stolen in 1998 and was eventually recovered by British paleontologist David J. Ward with the assistance of an anonymous fossil dealer. In his 1899 observations, Karpinsky also noted that the specimen described by Woodward in 1886 showed sufficient similarities with the Krasnoufimsk material to justify its provisional reassignment to Helicoprion, renaming it H. davisii. However, this interpretation was challenged as early as 1902 by American paleontologist Charles R. Eastman, who assigned the species to Campyloprion, a newly erected and closely related taxon. A few years later, in 1909, his colleague Oliver Perry Hay transferred the species once again, this time to Toxoprion, another newly established, related genus. In later publications, Karpinsky reaffirmed the position he had argued in 1899, an interpretation followed by several authors in the subsequent decades. His interpretation was finally confirmed in 1940, when German–American paleontologist Curt Teichert described much more complete fossils of H. davisii, which like the holotype, were also discovered in Western Australia.

Since the genus Helicoprion was established by Karpinsky in 1899, numerous additional species have been described from fossils found across the world, although most originate from North America. In a morphometric revision published in 2013, American paleontologists Leif Tapanila and Jesse Pruitt reassessed all of these historical species assignments. Their analysis showed that, among the roughly 10 named species, only three possess features distinctive enough to be considered valid: H. bessonowi, H. davisii, and H. ergassaminon, with the remaining taxa regarded as either synonymous or doubtful. H. ergassaminon was first described in 1966 by Danish ichthyologist Svend Erik Bendix-Almgreen in a monograph devoted to several Helicoprion fossils housed in the paleontological collections of various universities in Idaho, USA. As with the generic name, the specific epithet derives from the Ancient Greek ἐργασάμενον (ergasamenon), meaning "the one who has done work", in reference to the distinctive wear marks observed on the holotype. This latter, nicknamed "Idaho 5" and discovered in a now-abandoned mine near Fort Hall, was reported by Bendix-Almgreen to be stored at the University of Idaho in Moscow, Idaho. However, later searches failed to locate the specimen at that institution, and the fossil was subsequently considered lost. The holotype was finally rediscovered in 2017 during the recataloguing of the fossil collections at the Natural History Museum of Denmark, before being transferred in 2023 to the Idaho State University in Pocatello, where it is now held.

In his 1907 and 1909 works, Hay erected a new genus and species of eugeneodont, Lissoprion ferrieri, which he described from three fossil specimens originating from phosphate deposits along the Idaho–Wyoming border. The holotype consists only of a short series of three teeth, but one of the additional specimens illustrated in 1909 shows at least two tooth rows, leading Karpinsky to reclassify the taxon as H. ferrieri in 1911, while noting its resemblance to H. davisii. For nearly a century, this species was distinguished on the basis of tooth angle and height. However, in their 2013 revision, Tapanila and Pruitt demonstrated that these traits vary naturally within a single Helicoprion species, so regarded H. ferrieri as a junior synonym of H. davisii. In 1939, American geologist Harry E. Wheeler named two additional Helicoprion species, H. sierrensis and H. nevadensis, based on type specimens from California and Nevada, respectively. Wheeler distinguished H. sierrensis by the degree of variation in the shaft of the tooth whorl, whereas H. nevadensis was characterized, in his view, by the expansion pattern of the whorl and tooth height. In their 2013 revision, Tapanila and Pruitt demonstrated that the characters attributed to H. sierrensis fall within the natural range of variation seen in H. davisii, while those of H. nevadensis correspond to the growth stage of H. bessonowi. The two species named by Wheeler were thus synonymized with H. davisii and H. bessonowi.

In 1945, geologist Federico K. G. Müllerried described the species H. mexicanus on the basis of a poorly preserved partial tooth whorl bearing 10 teeth, discovered in the Mexican state of Coahuila. The author distinguished the taxon by the ornamentation of its teeth. Although the holotype of this species has since been reported lost, Tapanila and Pruitt noted that its anatomy closely resembles that of the largest known Helicoprion specimen. Nevertheless, neither specimen can be assigned to any of the three recognised species due to their incomplete preservation. Consequently, in the absence of more complete material attributable to the taxon, H. mexicanus is regarded as a nomen dubium. In 1953, Obruchev illustrated in his monograph a poorly preserved fossil specimen preserving the impression and root of two teeth, discovered in the Ural Mountains of Russia. Contrary to ICZN requirements, though, the author provided no diagnosis establishing the distinctiveness of the taxon. As the specimen is also considered lost, Tapanila and Pruitt classified this species as a nomen nudum. In 1970, Polish geologist Stanisław Siedlecki [pl] named the species H. svalis on the basis of isolated teeth and fragmentary tooth whorls recovered from the Norwegian archipelago of Svalbard. From the type specimen, he distinguished the taxon by the relative narrowness of the teeth, which appeared not to contact one another. Tapanila and Pruitt interpreted these observations as an artefact of the holotype’s partial preservation, since only the central portions of its teeth are preserved. The authors of the 2013 revision considered H. svalis to be strongly similar to H. bessonowi, but could not formally synonymise the two due to the incompleteness of the fossil material, so regarded it as a doubtful taxon.

In 2007, palaeontologist Xiao Hong Chen and colleagues described the species H. jingmenense from an almost complete tooth whorl discovered during road construction in Hubei Province, China. Although the authors noted close similarities to H. bessonowi and H. ferrieri, they distinguished their species from the former by having fewer than 39 teeth per volution, and from the latter by possessing broader cutting edges and a shorter compound root. In their 2013 revision, though, Tapanila and Pruitt pointed out that the specimen is partially obscured by its surrounding matrix, which likely led to an underestimation of tooth height. Taking this into account, along with intraspecific variation, they regarded H. jingmenense as a junior synonym of H. davisii.