The Tellarites were conquered some time following the conquest of the Alpha Centaurans in 2074. Although technologically savvy and costing the empire many lives to subdue, the Tellarites were eventually brought to kneel. Following their surrender, they were offered client status where they would allowed to live so long as they willingly gave over their special skills to the benefit of the empire. Continuous threats regarding the destruction of their homeworld should their engineering ingenuity ever fail resulted in the quick advancement of the empire's technology. (Decipher RPG module: Through a Glass, Darkly)
Major Malcolm Reed and Doctor Phlox of the ISS Enterprise tortured a Tellarite crewman named Terev in the agony booth as a demonstration of the device for Captain Maximilian Forrest and Commander Jonathan Archer. Reed's philosophy on Tellarites was that they were "all guilty of something".
At one point, frustrated with a lack of progress while trying to apprehend the rogue Gorn Slar aboard the stolen USS Defiant, Archer raged that "we'd have more luck sending a squad of Tellarites to capture this thing!" (ENT episode: "In a Mirror, Darkly")
With the rise of the Klingon-Cardassian Alliance in 2295, the Tellarites would suffer even more than they had under the empire. As the Alliance found Tellarites to be far too argumentative and difficult to deal with, they were openly attacked and reduced to only a few hundred thousand by the 2360s and 2370s. (Decipher RPG module: Through a Glass, Darkly)