Any shark is fair game, but some species are more prized than others. The large fins of Whale Sharks, Basking Sharks are coveted. Ironically, these species are among the most threatened. Pelagic species such as Blue sharks, Oceanic White tip are common, however, several illegal fisheries such as those that target the Galapagos and other remote islands will capture reef sharks and hammerhead sharks.
By nature, sharks are difficult to study and good fisheries data are hard to obtain. The practice of finning, which is mostly an unreported practice is robbing scientists of population and capture data. Many pelagic shark species are widespread and do not school. Many larger sharks travel vast distances alone. Most large sharks have late onset of fertility (decades) give birth to few young and have long gestation periods, making them very vulnerable to overfishing. Therefore, it is very difficult to arrive at a sustainable number. This is why most commercial shark fisheries collapse economically.
With accurate population numbers, a good understanding of the target shark’s biology, and accurate reporting of animals captured, a sustainable fishery might be achieved. Until that is achieved and it can be enforced, then the source of fins must stop and fins made illegal.