[Direct Quote from Wookieepedia]
Late Republic Era
Black Sun existed in some form or another for centuries. Although headquartered on Coruscant, its influence stretched the breadth of the Galaxy. Around 32 BBY the Black Sun was headed by Alexi Garyn, who was killed by Darth Maul on his master's orders. Below the leader of Black Sun were nine Vigos (Old Tionese language for "nephew"). Each Vigo ruled over their own territory and sector.
In the Clone Wars, Black Sun was dealing extensively with the plant bota, which was found on Drongar. Originally, Admiral Tarnese Bleyd was the main contact with Filba the Hutt for the smuggling. He was later assassinated by Kaird, a Nediji, following the death of the former operative Mathal. Another partnership was later established with Thula and Squa Tront to secure the bota. Upon learning that the bota was losing its potency, Kaird escaped from Drongar with a supply as a gift for his Vigos; it was subsequently discovered that the case was filled with explosives, in attempt at betrayal by Thula and Tront.
After The Rebel Alliance destroyed the Death Star I, Tyber Zann was left in control of a large fleet of Black Sun pirate ships.
Rise of the Empire
During the early days of The Galactic Empire, Black Sun was led by Dal Perhi, though his mantle was soon usurped by a Black Sun Captain named Xizor. The reptilian Falleen crimelord continued to lead Black Sun into the Galactic Civil War. Under Xizor's leadership, Black Sun became so powerful that the Prince was considered by some Coruscant courtiers to be surpassed in power by only Emperor Palpatine and Darth Vader.
Rivalry between Vader and Xizor was especially strong due to the fact that, after an accident at a biological weapons laboratory on Xizor's homeworld Falleen, Vader ordered all the Falleens who had been contaminated to be "sterilized" (i.e. they were killed). Xizor also dealt with a rival criminal organization, the Zann Consortium, using them to steal tibanna gas from a mining facility on Bespin owned by the Empire. Tyber Zann, leader of the Zann Consortium, betrayed Xizor by planting evidence that pointed the theft to the Black Sun. When Xizor learned that Luke Skywalker was Vader's son, he decided to kill Skywalker so as to foil Vader's plan to turn Luke to the dark side of the Force and embarrass him in the eyes of the Emperor. However, when Vader learned of the scheme, he made sure Xizor paid with his life.