Vault-Tec Corporation

Vault-Tec is the corporation that was contracted by the United States Government before The Great War to design and produce the Vault system. The Vaults were never intended to save the population of the United States. With a population of almost 400 million by 2077, the U.S. would need nearly 400,000 Vaults, and Vault-Tec was commissioned to build only 122 such Vaults. The real reason for these Vaults was to study pre-selected segments of the population to see how they react to the stresses of isolationism and how successfully they re-colonize after the Vault opens.

Future-Tec, a division of Vault-Tec, developed the G.E.C.K., the Garden of Eden Creation Kit for use by vault residents.

Like many major military contractors, as Vault-Tec grew in finances and responsibility, it began to develop highly experimental and secure technologies. In time, Vault-Tec was so thoroughly integrated with top-secret military research, it was practically a division of the U.S. government … almost. The company still retained some elements of privatization. So the principals of Vault-Tec - executives, scientists, and so on - had to be aware of the true function of the Vaults, and they had access to the technology. They were the developers. Regardless of the U.S. government's directives, Vault-Tec was not going to submit to a lottery and live underground with a bunch of human cattle in facilities that were intentionally defective. Thus Vault-Tec created their own facilities, removed from the larger Vault network - and kept secret from the U.S. government.

Vault-Tec didn't stop there. These secret, private installations were used to research the latest vault mechanisms as well as technologies that would benefit mankind in a post-nuclear environment. This, of course, included some extensive research with FEV.

No one can say for certain how Vault-Tec obtained FEV. Some think they had it all along, gaining it in a deal with the government, others think it was stolen from the government while VT was repairing one of the more guarded vaults.

Inconsistencies
Note that the company is sometimes referenced as Vault-Tek. While the first paragraph of Fallout: Brotherhood of Steel backstory for Vault-Tec sounds reasonable, the part about the company acquiring FEV does not fit into the Fallout canon.

Appearances in games
Vault-Tec Vaults and other technology appear in all Fallout games.