Tiburonian society included tribal structures. At some point in Tiburonian history, Zora conducted gruesome experiments on the body chemistry of several subject tribes of Tiburonians. Her work and methods were condemned by later generations, and in the 23rd century, she was seen as one of the most evil members of the Tiburonian species. (TOS: "The Savage Curtain")
In 2149, Tiburon hosted an Interspecies Medical Exchange conference. While Denobulans and Mazarites were present, no Klingon representatives were invited (although one Klingon was disguised as a member of the Mazarite delegation). (ENT: "Affliction")
Anatomy and physiology
The males of the species were bald and had unusually shaped ears. (TOS: "The Way to Eden") Female Tiburonians had either Caucasoid or greenish skin, long hair, and enlarged eyebrows. (TOS: "The Savage Curtain") Some males did not have eyebrows and had a small ridge-line across their foreheads. (DS9: "The Ship")
This species wasn't named in the script of "The Way to Eden".
Zora, seen in "The Savage Curtain", was never said to be a Tiburonian; it was merely said that she performed experiments upon the natives. However, the final draft script of "The Savage Curtain" identified her as a "Tiburon".
The species was named "Tiburonian" in the final draft script of "The Ship". 
The Worlds of the Federation described Tiburons as mutated descendants of Terran Humans.
The Decipher RPG book Starfleet Operations Manual used the name "Tiburonese". Modern Tiburonese are described as hybrids of native Tiburonese and the Ucali, a species that conquered Tiburon 1,400 years ago. The Ucali were aggressive conquerors who considered physical pleasure to be taboo, but over time, the native Tiburonese were able to tempt their conquerors into a life of pleasure. Modern Tiburonese culture is devoted to experiencing joy and the Tiburonese rely on robots to perform almost all economic activities.