The Tleilaxu are best known for their use of the axolotl tanks, which are essentially human uteruses kept on life support. The axolotl tanks grow many products used in the Imperium, including gholas, slig meat, and artificial organs (especially eyes).
At the end of the reign of Emperor Elrood IX, he conspired with the Tleilaxu at the behest of Hasimir Fenring to stage a takeover of the planet Ix, formerly held by House Vernius. The Tleilaxu required possession of this planet to begin research on synthesizing melange. This project ultimately bore no fruit, and ended in an uprising of the Ixian people led by Prince Rhombur Vernius and Duke Leto Atreides of Caladan.
Though many worlds of the Imperium use Tleilaxu goods, they are not trusted. Much of this is because of their capabilities. Part of the Tleilaxu race are Face Dancers which can emulate the looks of any being of approximate size, and with study and training can emulate their demeanor as well. However, it cannot be discounted that in general, the Bene Tleilax hold most of humanity in contempt. As a result, the Tleilaxu have never been permitted to hold a seat in the Landsraad council, although they are nominally part of the Imperium.