Sleuthing Sharks in the Fishmonger's Stall

When I first started reading about sharks, back in the 70s, people talked about 300 species.  Then 350, then 400, and experts now make estimates of 440 all the way up to 470, with the usual allowances that some species may turn out to be variations of known species - and the reverse. 
Where do you find new sharks? 
Some are split out from studies of known species. 
Occasionally scientists just get lucky, as when the most spectacular modern discovery, the megamouth shark, was caught in a parachute being used as a sea anchor by a Navy ship in 1976. (What is truly weird about that is that some 70 specimens have been caught of found stranded since: where was it until 1976? You can't mistake it for any other shark.  Hmmm.....  an excellent article from Scientific American is found here.)
Many turn up in fishermen's catches.  Some are spotted at sea by scientists with fishing fleets or fishermen themselves.  

Megamouth shark (Megachasma pelagios.) This one was found off Florida, a continent away from the first discovery in the Pacific. (Florida Museum of Natural History)

Sorting through the catch fishing boats haul to docks and markets, though, is probably the most  effective technique.  After all, that's how the most famous fish discovery in history, the coelacanth, turned up in 1938.
This article from Smithsonian collects many other examples. Most stunning is that one David Ebert has named 42 species of sharks, rays, and chimeras.  Others have found more new species, species in ranges we didn't know they inhabited, and species unseen for many years. No one had seen a smoothtooth blacktip shark for over a century before Rima Jabado of the United Arab Emirates found one in 2009. 

Smoothtooth blacktip shark. (Source and copyright unknown: educational fair use claimed).

Humans, scientists and laypersons alike, are fascinated with sharks. Sometimes it's because sharks are beautiful and amazing: sometimes it's because people still believe all sharks are like the one in Jaws (despite the late Peter Benchley's spending the rest of his life on shark conservation). 
Shark fishing is often an unsustainable business, or an illegal one, but a shark that's on display in a market is gone, and there's no point in not gleaning knowledge from it. Shark biologists agree on one thing: we haven't found them all. 

If you want to see the most amazing photographs of these creatures and meet them closeup, Shark by photographer Brian Kerry  (National Geographic, 2017) is a stunning book. 

Other sources: 
"Rediscovery and redescription of the smoothtooth blacktip shark, Carcharhinus leiodon (Carcharhinidae), from Kuwait, with notes on its possible conservation status"
Alec B. M. Moore, et. al.,   
Marine and Freshwater Research 62(6) 528-539 https://doi.org/10.1071/MF10159

 Published: 24 June 2011 .
Matt Bille, "The Still-Puzzling Coelacanth," Shadows of Existence, Hancock House, 2006. 
Florida Museum, :Megamouths," https://www.floridamuseum.ufl.edu/discover-fish/sharks/megamouths/