The name originates from the Permian genus Coelacanthus, which means hollow spine and was published by Swiss-born American biologist and geologist Jean Louis Rodolphe Agassiz in 1839.
The type species Coelacanthus granulatus was described from the Late Permian, Wuchiapingian of Kupferschiefer of Germany and England. Coelacanthus is primarily known from Late Permian and Early Triassic deposits in Europe and Canada, although the referred species C. welleri, known from Iowa, is of Late Devonian, Famennian age. They survived the Permian–Triassic extinction event, and one species, C. banffensis, is known from the Early Triassic.
Coelacanths belong to the subclass Actinistia, a group of lobed-finned fish related to lungfish and certain extinct Devonian fish such as osteolepiforms, porolepiforms, rhizodonts, and Panderichthys. The oldest known coelacanth fossils are over 410 million years old. Coelacanths were thought to have become extinct in the Late Cretaceous, around 66 million years ago, but were rediscovered in 1938 off the coast of South Africa.
Coelacanths follow the oldest-known living lineage of Sarcopterygii, lobe-finned fish and tetrapods, which makes them are more closely related to lungfish and tetrapods — which includes amphibians, reptiles, birds and mammals — than to ray-finned fish. They are found along the coastline of Indonesia and in the Indian Ocean. The West Indian Ocean coelacanth is a critically endangered species.
The coelacanth was long considered a living fossil because scientists thought it was the sole remaining member of a taxon otherwise known only from fossils, with no close relations alive, and that it evolved into roughly its current form approximately 400 million years ago. Several more recent studies have shown that coelacanth body shapes are much more diverse than previously thought.