|The following is based on Fallout: Brotherhood of Steel and has not been confirmed by canon sources.|
The following is transcribed from the Fallout: Brotherhood of Steel manual. The manual is included in the references.
In a future not far removed from our own, a world filled with marvel and wonder is shaken to its very foundations by the greed and destruction of mankind. Atomic war, the once impossible threat, has been unleashed and the face of the world has been scarred forever. Endless deserts and the twisted remains of our past are all that stand in the wake of the bombs. Small pockets of life, still driven by violence, scrape together a new world in the shadow of the old.
Fallout takes place many years after the apocalypse, as humanity struggles to pick up the pieces. Some groups have barely managed to survive above ground, either scavenging the scorched ruins of megacities or surviving and adapting through mass mutation. Communities that were sealed in underground vaults during the war are now emerging to re-populate the blasted landscape.
Welcome to the wasteland. 
The Great War
The war that devastated the majority of the world population in a global nuclear conflict was primarily a resource war. As fuel reserves dwindled, the major super power attempted to gain control of them, leading to a course of events that would change the very face of the planet...
In 2025, as the planet's resources dried up, the United Nations fell apart, causing many smaller nations to fall with them as financial havoc swept across the globe. The handful of peace agreements between Europe and the Middle East were cast into a long, drawn-out war over the few remaining productive oil fields.
By late 2035, after the threat of a recently discovered super plague and the destruction of Tel Aviv by a terrorist nuclear weapon, the United States of America closed its borders. In early 2054, the U.S. created "Project Safehouse". Financed by junk bonds, this plan was responsible for creating large underground survival shelters, known as vaults. Unfortunately, the money ran out 9 years later and the project was left incomplete, shortly after the Middle Eastern oil fields ran dry and the European War ended.
In the winter of 2066, China attacked Alaska over the last drops of oil in the world. In a desperate maneuver, both superpowers invaded neighboring countries in an effort to bolster their dwindling resources. The U.S. annexation of Canada was concluded by 2076. Canadian timber provided fuel for U.S. military needs, and Alaska was reclaimed by early 2077.
In the early morning hours of Saturday, October 23, 2077, the sky was filled with nuclear missiles. Because of frequent false alarms, few made it to the Vaults when the final alarm sounded. Most people were trapped outside the closing Vault doors. No one knows who started the war, but after two hours of nuclear devastation, no one cared.
Developed by a miliatary contractor called Vault-Tec, the Vaults were underground shelters meant to preserve Americans in the event of a nuclear war. At least, that was their official purpose. With a population of almost 400 million by 2027, the U.S. would have needed nearly 400,000 Vaults to safely shield every man, woman and child. In reality, Vault-Tec was commissioned to build only 122 Vaults, in order for the US government to study pre-selected segments of the population to see how they react to the stresses of isolationism.
Like many major military contractors, as Vault-Tec grew in finances and responsibility, it began to develop some highly experimental technologies. In a short amount of time, Vault-Tec was so thoroughly integrated with top-secret military research it was practically a division of the U.S. government... almost. Unknown to their financial backers, Vault-Tec created their own facilities, independent from the larger Vault network and kept secret from the U.S. government.
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. And this included some extensive research into a substance classified as FEV.
FEV & The Brotherhood
FEV [Forced Evolutionary Virus] was initially developed in response to the "super plague" that tore through the world population prior to the Great War. Designed to push any biological entity's ability to adapt to harsh circumstances, the substance was found to possess startling abilities as a catalyst.
Early tests created super animals - lab monkeys with greater body mass and higher intelligence. The military immediately saw some possible applications and took control of FEV research. Unfortunately, the initial test subjects quickly regressed into a far less intelligent, aggressive state, showing massive deformities and insanity. FEV was labeled "unstable", but some experimentation still continued.
When the bombs dropped, one of the major military FEV research centers was hit, releasing huge quantities of the substance into the air. The mixture of heavy radiation and a sweeping cloud of mutagenic material turned large numbers of humans into Ghouls, and created Radscorpions, giant rats, and so on from the animals and plants across the U.S.
But the story of FEV doesn't end there. Even after the war, an isolated group of scientists began experimenting on soldiers with an advanced form of the virus [FEV-2]. The results were promising... but the surviving soldiers got wise. They rebelled, killed all of the scientists and locked down the facility. Relocating themselves and some high-tech equipment to a new base of operations, these soldiers took it upon themselves to become the unofficial peacekeeping force of the wasteland... they became the Brotherhood of Steel.