Not organized along feudal lines (as most of the rest of the Imperium is), the Tleilaxu are secretive and very little is known about them; however, in Heretics of Dune their society is said to be a meritocracy. They are chiefly known for their biological products, such as artificial eyes, gholas, and Face Dancers. Because they deal in morally-questionable but highly desired products, the Tleilaxu are universally distrusted but still influential.
The use of "Bene" before their name suggests that they are an order of some kind, like the Bene Gesserit; this becomes clear in the last two books of the original series, Heretics of Dune and Chapterhouse Dune.
Over 3,500 years later in God Emperor of Dune (1981), Tleilaxu Face Dancers kill and replace nearly everyone in the Ixian embassy on Arrakis as part of an assassination attempt on Paul's son, Leto Atreides II. The plot fails, in part due to the ingenuity of their own later generation of Duncan Idaho ghola.
Another 1,500 years pass, and in Heretics of Dune (1984) the core of the Tleilaxu is revealed: they are Zensufi, a distant offshoot of Buddhism and Sufism, and are organized along theistic lines. They have spent thousands of years concealing this fact, waiting for their ascendancy, which they believe to be occurring in Heretics of Dune. Their secret holy language is called Islamiyat, an ancient tongue the Bene Gesserit recognize and employ to elicit trust from the Tleilaxu. The Bene Gesserit pretend to share the Tleilaxu "Great Belief, the Sufi-Zensunni ecumenism that had spawned the Bene Tleilax. The Tleilaxu now provide the Sisterhood with Idaho gholas, and in Heretics of Dune it is also revealed that the Tleilaxu have developed the ability to grow the spice melange in the same axlotl tanks they use to grow gholas.
By the events of Chapterhouse: Dune, the Bene Tleilax have been all but eradicated by the fierce Honored Matres save for one Master, Scytale; he is a ghola of the original Scytale of Dune Messiah, somehow having ascended from Face Dancer to Master. Captured by the Bene Gesserit, Scytale's secret bargaining tool is a hidden nullentropy capsule containing cells carefully and secretly collected by the Tleilaxu for millennia, including the cells of Tleilaxu Masters, Face Dancers, Paul Atreides, Lady Jessica, Chani, Gurney Halleck, Thufir Hawat and other legendary figures. He intends to not only grow his own life-sustaining ghola, but to resurrect the rest of his order as well. In the meantime, he has given the Bene Gesserit enough of the axlotl technology to grow their own gholas, in particular a replacement for their military genius Miles Teg.
An axlotl tank is essentially a brain-dead woman whose womb is used as a tank to create gholas. The Bene Tleilax's use of their women in this capacity explains why no one has ever seen a Tleilaxu female.
In Heretics of Dune, it is revealed that the Tleilaxu have developed the ability to grow the spice melange in axlotl tanks, breaking the monopoly on spice that Arrakis held for thousands of years which strongly controlled the economics and the politics of the Imperium.
In Chapterhouse Dune, the Bene Gesserit have acquired axlotl tank technology and are able to use it to make gholas for their own purposes, but not spice. They are revealed not to be tanks at all, but dramatically altered women.
The axlotl tank is similar to the reproductive "stumps" in Herbert's Hellstrom's Hive.
Chairdogs are also featured in Herbert's Whipping Star and The Dosadi Experiment. Neither of these books is connected with the Dune series.
Face Dancers are sterile creatures, with full sentience, but with a genetically programmed loyalty to the Tleilaxu Masters. They are able to physiologically change their appearance to impersonate other people. They are used by the Tleilaxu throughout the universe to replace people whom the Tleilaxu find useful (the originals are usually killed). In this way they may infiltrate and control various groups in the universe.
Over the course of the series, as the Tleilaxu try to create more perfect mimics, the Face Dancers gain the ability to even absorb the consciousness of their subject, with the potential unintended side effect of gradually becoming that person, and passing beyond the control of the Tleilaxu Masters, rendering them useless for any purpose other than living out the rest of their subject's life just as they would have on their own.
Tleilaxu Masters control their creations by forcing them into a hypnotic state with some predefined, implanted sound (often a specific humming or whistling noise). In Dune Messiah, the Tleilaxu dwarf Bijaz controls the ghola Hayt through a specific humming intonation that renders Hayt open to implanted commands. In Heretics of Dune, the Master Waff attempts to control his perfectly mimicked Face Dancer copy of High Priest Tuek with a humming language, but fails due to the copy's complete assimiliation into its new form.
Notable Tleilaxu Masters include Master Hidar Fen Ajidica, Master Scytale and Master Tylwyth Waff. Masters Mirlat and Torg the Younger also appear in Heretics of Dune.
A Contaminator is essentially a hideously-deformed mutant spawned from the Tleilaxu Flesh Vats. It carries a lethal virus, capable of turning human beings into additional Contaminators. Any infantry killed in close combat with a Contaminator will be reborn as a Contaminator, under the command of the player controlling the original Contaminator. The Contaminator is only effective against infantry, however; its attack is extremely weak against enemy vehicles and structures.
The other unit of the Bene Tleilax forces offered to the three Great Houses during the War of Assassins, the Tleilaxu Leech, is a biogenetic tank that creates replicas of itself by implanting its larvae in enemy vehicles. It constantly damages the host vehicle until the target is destroyed and the larva hatches as another Leech. The infant larva can be removed by attacking the host vehicle or by using an infantry engineer to remove it surgically (the Atreides can also use their Repair Vehicle). A leech is extremely fast and can regenerate while stationary, making it efficient for hit-and-run tactics.