The Vault-Tec Corporation is the main antagonistic group of the Fallout game series. It was a company contracted by the United States Government in the years leading up to the Great War to produce a series of underground fallout shelters in the event that War did indeed go nuclear.
These fallout shelters, colloquially referred to as "Vaults" were designed and spread across the country, had a far more devious purpose than protecting the human race from nuclear annihilation. They were, in fact, secret experiments designed by the United States Government to test the effects of various factors on humans.
Fallout 3, shows several of these Vaults located around the Washington D. C. area. Inhabitants of Vault 87 were exposed to the Forced Evolutionary Virus (FEV), which caused rapid mutations, and was responsible for creating the East Coast breed of Super Mutants. Vault 92, claiming to be a shelter to preserve artistic talents was, in actuality, a program designed to see if white noise could be used to brainwash people into becoming super-soldiers. Vault 101, where the game begins, was designed with a "never leave" policy in mind, and to study the effects of an omnipotent dictator controlling every aspect of daily life.
In Fallout: New Vegas, Vault 3 is seen to be one of the few "control vaults" where no experiments take place. The inhabitants, however, were eventually overrun by the Raiders now operating out of the Vault. Vault 22 was designed with the purpose of sustaining inhabitants solely on crops grown within the confines of the Vault; fungal spores, however, mutated the occupants into "Spore Carriers," a carnivorous human/plant hybrid creature.
While most Vault Experiments ended in failure, Vault 21, built under the Las Vegas Strip, was actually a success. Vault 21 was designed with the purpose of solving all problems through gambling, and all of the candidates "selected" for entry were gambling addicts. Since the end of the Great War, it has been converted into a Casino/Resort on the New Vegas Strip.
Fallout 4 shows more of these Vaults located around the Boston area. Vault 111's inhabitants were subjected to long-term cryogenic suspension under the pretense of being "decontaminated". The Vault staff eventually became split into two factions; those who sided with the Overseer in keeping the Vault closed (due to them receiving no All-Clear Signal following the mandatory shelter period, leading them to believe that the radiation outside had not declined enough to be survivable), and the Vault security staff who desired to leave the Vault due to dwindling supplies. This resulted in a mutiny that left the test subjects unattended, leaving them frozen for over 200 years.
Vault 95 was populated solely by drug addicts. Five years after the vault was sealed, a hidden stash of drugs was unlocked. Within a few days, all of the vault residents but one fell back into addiction or killed each other. By the time of the game, Vault 95 is inhabited by Gunners, and the Sole Survivor travels there to cure their companion Cait of her chem addictions.
Vault 81 was initially built for the purpose of creating a single cure for all diseases. Unlike the other vaults however, Vault 81's residents were saved from the hideous experiments of the Vault-Tec scientists thanks to the original overseer's sudden change of heart by having the equipment disabled which would have otherwise allowed the scientists to expose the residents to diseases.
Vault 75 was built underneath Malden Middle School, and was advertised as a shelter for the school's students and their families. However, upon entering the Vault, the parents were separated from the children and executed by the security staff. Vault 75's purpose was to enhance the gene pool of the residents to create stronger and more intelligent subjects. To achieve this goal, the children were tested both mentally and physically to the point of borderline torture, and were told that upon 'graduation' when they turned eighteen, they would be released to help the people of 'Uptopland' (a nickname the residents gave to wasteland). Those with exceptional intelligence and physical health were harvested for there genes, more intelligent subjects who displayed obedience were recruited to the Vault's science team, and those who did not meet expectations were killed following their graduation ceremony. By the time of the game, Vault 75 has been emptied and is now used as a stronghold by the Gunners, like Vault 95.