Though not used in a great number of episodes, they are one of the founding races of the show's United Federation of Planets, to which Earth belongs. Notable Tellarites include Ambassador Gav (from the original Star Trek episode "Journey to Babel"), bounty hunter Skalaar, and his brother Gaavrin (both from Star Trek: Enterprise).
Tellarites are a porcine-humanoid species. They have black pupils set in deep eye sockets and large snouts. Tellarites are very hairy; besides having beards and large bushy hair, they also have coarse pinkish-brown skin. In Star Trek: The Original Series they are portrayed as having three fingers, but in Star Trek: Enterprise, not only is their facial makeup updated, they also have five fingers. Overall the depiction in the original series is different from the Enterprise depiction, but this can easily be explained as simply due to the limitations of makeup in the sixties. In Star Trek: The Original Series there was also one small inconsistency of the Tellarite hands. One Tellarite seen in the episode "The Lights of Zetar" had hands with 4 fingers and a thumb, while all other Tellarites seen throughout the entire series had hands with only 2 fingers and a thumb. There is still some debate among fans as to whether or not the alien seen in the episode was even a Tellarite at all. Regardless, it should be noted that the producers of Star Trek: Enterprise probably simply forgot to give the Tellarites back their original hands. Tellarites prefer temperatures slightly above human standards.
Tellarites were warp-capable at least since the 20th century, but they only made contact with humans on March 21, 2153, by the Starfleet ship Enterprise NX-01. Although this encounter was rather hostile (a Tellarite bounty hunter kidnapped Captain Archer), the relations between humans and Tellarites apparently improved in the next few years until both species became founding members of the United Federation of Planets in 2161. A key moment in this process was an incident in 2154, when humans forced them to work together with their enemies the Andorians to prevent a Romulan attempt to destabilize the region. For the next several hundred years, Tellarites continued to be an important species in the Federation (although they were only rarely seen onscreen). By 2267, in the TOS episode "Journey to Babel", the Babel Conference, which included many Federation worlds including Tellar, was considering the fate of the disputed world Coridan, with its rich mining resources.
Gav, leader of the Tellarite delegation, made heated charges that other ambassadors were either hindering or actively seeking the Tellarites' removal of any say in the negotiations. He accused Vulcan ambassador Sarek of the most serious charges. Gav suddenly turned up in one of the Enterprise's Jefferies tubes, dead of an apparent Vulcan killing technique, snapping his neck. The subsequent investigation uncovered a plot by the notorious Orion species to break up the conference, frame Sarek for the killing of Gav, and claim Coridan by deception.
The Tellarites were described by Sarek in "Journey to Babel", as being argumentative, not to make a point, but simply to argue. Hailing from Tellar Prime, they built a trade empire for dozens of light-years around their homeworld, by both hard negotiation and combat. Despite a reputation for being tough and ruthless, the Tellarites were honor-bound in their business dealings.
In combat, however, despite local success, the Klingons of Deep Space Nine found them easy prey. During the 2373 Klingon-Federation conflict, one Klingon captain boasted of decapitating a Tellarite helmsman, saying of the victim "The pig barely had time to raise his weapon."
Tellarites are renowned for being rather direct and forceful in conversation, and are known to be so quarrelsome that arguing is a sport on their home planet, Tellar. They consider normal polite conversation to be a grave insult; it is recommended to be insulting and crude when speaking to a Tellarite. Because of their ability to argue, Tellarites make excellent politicians. They like taking muddy baths. However, Tellarites take great umbrage if compared to the habits of Terran swine, saying they in particular are not food.
The non-canon fan-produced webcast series Star Trek: Hidden Frontier has featured Tellarite culture prominently. A Tellarite medical officer, Henglaar, features a variation of the TOS look of the species. Henglaar is described at the  website as being "curmudgeonly", and "an expert on how not to be married".
As of 2153, the Tellarites have more advanced ships than Earth; even their smaller shuttlecraft can attain speeds of warp 4 (around 64 times the speed of light on the old warp scale, 101 times on the new one). During the Babel Crisis episodes on Enterprise, it was stated by Ambassador Gral that the Tellarites were less advanced than the Andorians.