There are fifteen species belonging to the genus Eurypterus, the most common of which is Eurypterus remipes, the first eurypterid fossil discovered and the state fossil of New York.
Members of Eurypterus averaged at about 5 to 9 in (13 to 23 cm) in length, but the largest individual discovered was 1.3 m (4.3 ft) long. They all possessed spine-bearing appendages and a large paddle they used for swimming. They were generalist species, equally likely to engage in predation or scavenging.
The first fossil of Eurypterus was found in 1818 by S. L. Mitchill, a fossil collector. It was recovered from the Bertie Formation of New York (near Westmoreland, Oneida County). Mitchill interpreted the appendages on the carapace as barbels arising from the mouth. He consequently identified the fossil as a catfish of the genus Silurus.
It was only after seven years, in 1825, that the American zoologist James Ellsworth De Kay identified the fossil correctly as an arthropod. He named it Eurypterus remipes and established the genus Eurypterus in the process. The name means "wide wing" or "broad paddle", referring to the swimming legs, from Greek εὐρύς (eurús, wide) and πτερόν (pteron, wing).
However, De Kay thought Eurypterus was a branchiopod (a group of crustaceans which include fairy shrimps and water fleas). Soon after, Eurypterus lacustris was also discovered in New York in 1835 by the paleontologist Richard Harlan. Another species was discovered in Estonia in 1858 by Jan Nieszkowski. He considered it to be of the same species as the first discovery (E. remipes); it is now known as Eurypterus tetragonophthalmus. These specimens from Estonia are often of extraordinary quality, retaining the actual cuticle of their exoskeletons. In 1898, the Swedish paleontologist Gerhard Holm separated these fossils from the bedrock with acids. Holm was then able to examine the almost perfectly preserved fragments under a microscope. His remarkable study led to the modern breakthrough on eurypterid morphology.
More fossils were recovered in great abundance in New York in the 19th century, and elsewhere in eastern Eurasia and North America. Today, Eurypterus remains one of the most commonly found and best known eurypterid genera, comprising more than 95% of all known eurypterid fossils.
The genus Eurypterus belongs to the family Eurypteridae. They are classified under the superfamily Eurypteroidea, suborder Eurypterina, order Eurypterida, and the subphylum Chelicerata. Until recently, eurypterids were thought to belong to the class Merostomata along with order Xiphosura. It is now believed that eurypterids are a sister group to Arachnida, closer to scorpions and spiders than to horseshoe crabs.
Eurypterus was the first recognized taxon of eurypterids and is the most common. As a consequence, nearly every remotely similar eurypterid in the 19th century was classified under the genus (except for the distinctive members of the family Pterygotidae and Stylonuridae). The genus was eventually split into several genera as the science of taxonomy developed.
In 1958, several species distinguishable by closer placed eyes and spines on their swimming legs were split off into the separate genus Eiropterus by Erik Kjellesvig-Waering. Another split was proposed by Lief Størmer in 1973 when he reclassified some Eurypterus to Baltoeurypterus based on the size of the some of the last segments of their swimming legs. O. Erik Tetlie in 2006 deemed these differences too insignificant to justify a separate genus. He merged Baltoeurypterus back into Eurypterus. It is now believed that the minor variations described by Størmer are simply the differences found in adults and juveniles within a species.