Coelacanths are lobe-finned fish, which vary in size but can reach up to 6.4 feet in length and weigh up to 176 pounds. Scientists have inferred that they can live 80 to 100 years. Their closest living relatives are lungfish and as fossils they can be readily identified by their distinctive ‘tail flag’. They were long thought to be extinct because their fossil record seems to disappear quite abruptly along with the dinosaurs and many other creatures at end of the Cretaceous period, 65 million years ago. 
In the winter of 1938, trawler captain, Hendrik Goosen returned to London after an excursion to South Africa’s Chalumna River. He contacted friend and curator, Marjorie Courtenay-Latimer, beacause she delighted in looking through his exotic catch for anything interesting. She noticed a distinctive fish, which she described as "the most beautiful fish I had ever seen, five feet long, and a pale mauve blue with iridescent silver markings."
She could not identify the fish from any of her conventional texts so she tried to contact her friend and colleague, James Leonard Brierley Smith. Since he was on Christmas holidays, she sent the fish off to a taxidermist so it could be preserved until his return. When Smith saw the specimen, he immediately recognized the distinctive tail flag of the coelacanth, which until that point, he had only seen as a fossil. This specimen,which he named Latimeria chalumnae to honor Marjorie Courtenay-Latimer, can still be seen in the East London Museum.
A worldwide search for more coelacanths advertised a reward of £100 but it took 14 years for another discovery to be made in the Comorian islands. The locals all knew of the coelacanth, as it occasionally appeared in fishermen’s catches but they always threw it away as it is inedible.
The coelacanth proved to be elusive animal because its natural habit is deep ocean. Some species have been found over 2000 feet below. Coelacanths are now known in the Comoros, Indonesia, Kenya, Madagascar, Mozambique, South Africa, Tanzania. And now that the conservational value of the coelacanth is known by the Comorians, when they are accidentally caught, they are returned to deep water.
You can read Smith’s account of the coelacanth story in Old Fourlegs, which though published in 1956, is still in print. The coelacanth ahs also found its way into popular imagination through the years; I am a big fan of Ogden Nash and so thouroughly enjoyed this poem: 
Consider now the Coelacanth
Our only living fossil,
Persistent as the amaranth,
And status quo apostle.
It jeers at fish unfossilized
As intellectual snobs elite;
Old Coelacanth, so unrevised
It doesn't know it's obsolete.
- Ogden Nash
