Bill and Budd are brothers who grew up without a father (although Esteban Vihaio, a pimp, acted as a father-figure for a time). O-Ren Ishii was left an orphan after her parents were killed by Japanese crime boss Matsumoto.
They were, as their name suggests, an assassin squad, run and managed by Bill. He is known to have had a romance with Kiddo (his girlfriend and protégée, whom he impregnates}.
At the time of The Bride's revenge, the group has largely disbanded. Vernita lives as a housewife with a daughter, O-Ren is a crime boss in Tokyo, Budd is a bar bouncer, Bill is shown mostly as a retired killer to whom Elle remains fanatically devoted. The Bride has just recovered from a four-year coma, which started when the others came to her wedding rehearsal and killed the wedding party, but mistakenly left her alive. Bill delivers what he believes to be the coup de grâce as revenge for walking out on him. Their daughter is delivered while she is in a coma, and is being raised by Bill without her knowledge.
Although never explicitly said, it is widely held that Black Mamba is the most lethal and skilled of the Deadly Viper Assassination Squad after Bill himself, making her the deadliest woman on the planet. Many of them wield katana, and in the case of Bill and Budd, forged by Hattori Hanzō, an Okinawansword maker of legendary standing, who comes out of retirement to make his final masterpiece, The Bride's samurai sword. Bill, The Bride and Elle Driver are trained by Pai Mei, a Chinese martial arts master who is later poisoned by Elle Driver. Besides their training in the martial arts, they are also fluent in several languages, well-versed in the use of firearms, and skilled in various assassination, espionage, surveillance and weapon combat techniques. Some members seem to have personal specialties. O-Ren seems to favor ranged weapons (a sniper rifle in her flash-back and throwing darts in the confrontation at the House of Blue Leaves), Vernita favors close combat using knives (as stated by the Bride, quoting Bill) and Elle seems to favor poisons (she uses this tactic to kill Pai Mei in a flashback, attempted to use it against the comatose Bride, before Bill stopped her and arguably used it against Budd by way of the black mamba). Budd seems to favor firearms (he is seen carrying an AK-47 as the DeVAS approach and enter the Two Pines wedding chapel. Also he shoots a round of rock salt into the bride with his shotgun.) Bill and Kiddo never demonstrate a preference for any specific weapon or tactic, although Bill's codename (Snake Charmer) and the Deadly Viper Assassination Squad almost exclusively female membership may imply that Bill's speciality is his way with women.
Kiddo kills Green, Ishii and Bill in her quest for revenge. Budd is killed, fittingly, by a black mamba which Driver puts in a suitcase filled with money. It is left ambiguous whether Driver survives; she is left blinded and locked up with the black mamba that killed Budd, ranting and screaming in an isolated desert trailer. At the end of the film, all the characters who have been killed have their names crossed out on Kiddo's list, but Elle's name instead has a question mark over the top of it, suggesting that she could still be alive.
The five assassins of the Deadly Viper Assassination Squad are a reference to the Five Deadly Venoms, a group of five Hong Kong action actors employed by Run Run Shaw in many old Shaw Brothers martial arts films that were part of the inspiration for Kill Bill. The actors first worked together in a movie called The Five Deadly Venoms, and were referred to as such when seen in later movies together. In another Tarantino movie, Pulp Fiction, Mia Wallace (also played by Uma Thurman) states that she worked on a pilot episode of "Fox Force Five", which included five very different women with special talents that are similar to the talents of the Deadly Viper Assassination Squad. It was also mentioned in Pulp Fiction that her character was "the deadliest woman in the world with a knife", whereas in Kill Bill Vernita Green is described by The Bride as such. It is also of note that the list of names that Thurman's character makes in Kill Bill is titled "Death List Five". Tarantino also cited the 1973 Ted V. Mikels film The Doll Squad as an inspiration.
While Sofie Fatale is not an official member of the Deadly Viper Assassination Squad, she was at least involved in their operations and is in personal contact with Bill (who is mentioned to have previously been her mentor).
Bill has been shown telling at least three members of the Deadly Viper Assassination Squad that he loves them: The Bride, Elle Driver (on the phone) and Budd (on an inscription on his Hanzo sword).