This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
The Barzans were an intelligent humanoid species native to the planet Barzan II. The Barzans were governed by the Barzanian Planetary Republic, which was headed by a premier. In 2366, the premier was Bhavani. (TNG: "The Price")
Barzans had pairs of subtle ridges on their eyebrows and foreheads. Their blood was black in color. When leaving their homeworld, they relied on augmentation in the form of a breathing device that provided them with the gases found in the toxic atmosphere of Barzan II. (TNG: "The Price"; DIS: "Project Daedalus")
In 2366, a wormhole was discovered near their planet. The Barzans sent an automated space probe to collect data on the other end. They determined it was in the Gamma Quadrant, which was quite exciting since it meant they had a natural resource that other civilizations would invest in. It was hoped that the Barzan wormhole would open a new era in prosperity. This hope was a major factor in the Barzans' decision to sell rights to the wormhole to the highest bidder. Unfortunately, the wormhole turned out to be the "proverbial lemon", as the other end of the wormhole was not fixed, with one endpoint actually being in the Delta Quadrant. (TNG: "The Price")