NOTE: This article is about the incarnation of Brotherhood of Mutants from the X-Men film series. The mainstream version can be found here: Brotherhood of Evil Mutants.
The Brotherhood of Evil Mutants is an organization that served as recurring antagonistic group of the X-Men film series. It is an organization that was founded and led by Magneto as they vied for mutant supremacy and the destruction of the X-Men.
The Brotherhood was founded sometime around 1962 sometime after the Cuban Missile Crisis by Magneto. Following the death of Sebastian Shaw, the Hellfire Club had disbanded and the remaining members all joined up with Magneto and became the founding members of the brotherhood. The original brotherhood mainly consisted of Azazel, Angel Salvadore, and Riptide who were all former members of the Hellfire Club and Mystique was also recruited as well. Soon afterwards, the very first mission of the Brotherhood was to attack the CIA Headquarters and free Emma Frost and she eventually joined shortly afterwards. Most of the original members would be killed however between 1962-1973 with Operation Wide Awake killing Angel, Azazel, and Emma Frost. The fate of Riptide was unknown but Magneto and Mystique survived and went into hiding.
Decades later in the 21st Century, the mutants had became well-known by the general public and were vilified. The Brotherhood of Mutants had survived and were being lead by Magneto. Magneto and Mystique were back but the Brotherhood had also recruited Toad and Sabretooth into their ranks and were plotting to use Rogue, an X-Men member, to power a conversion machine to turn humans into mutants and this lead to both the Brotherhood and the X-Men fighting in New York City. Cyclops, Jean Grey and Storm fought Toad and the latter electrocuted Toad and killed him. Wolverine fought Sabretooth until the latter was knocked over the Statue of Liberty by Cyclops. Afterwards, Magneto was arrested and sent to a plastic prison and Mystique went into hiding.
X2: X-Men United
Sometime after Magneto's imprisonment, Mystique had returned and broke out Magneto to lead the Brotherhood once more. After stopping Stryker's plans to kill mutants along with the X-Men, Magneto and Mystique hijack the machine and switch it to kill humans instead before leaving. X-Men member Pyro during this time, becomes more sympathetic with the Brotherhood and its ideology and eventually joined the brotherhood after defeating Stryker, Pyro defected from the X-Men and joined the Brotherhood where he abandoned his birth name to become Pyro and fled with Magneto and Mystique.
X-Men: The Last Stand
Sometime in the 21st Century, the company Worthington Labs had managed to develop the Mutant Cure, a chemical that could successfully de-power and mutant temporarily and make them into a normal human. Knowing of this, Magneto had mobilized the Brotherhood where they managed to merge the Omegas group into their ranks and Magneto declared that mutants were the cure and instigated an all-out war against humanity. The Brotherhood then arrived in San Francisco where Magneto took the Golden Gate Bridge and used it to cross over to Alcatraz Island and engage both the X-Men and the United States Military in combat. During this time, Jean Gray had turned to the Brotherhood and was forced to be killed by Wolverine. Most of the Brotherhood members were killed or de-powered and after Magneto was cured, the Brotherhood was defeated and disbanded afterwards.
In the 1970s, Erik had been enraged at humankind for the abuse they've committed against mutants. Once being rescued by Charles, Erik states that mutants should rebel against humanity and cited the deaths of Azazel, Angel, and Emma Frost as examples of human atrocities against mutantkind. Charles refuses to give into such a dangerous ideology but Erik persisted and he eventually returned back to being Magneto. At a rally to show off the Sentinels to deal with the new mutant threat, Magneto appeared and took control over them and caged in the Richard Nixon and the White House with a baseball stadium. He then declared to humanity that mutants are the future and that all mutants must rise up and form a Brotherhood to resist human oppression.
In 1992 in the revised timeline, the Brotherhood of Mutants is a society of mutants based on the island of Genosha led by Magneto where they have built their own thriving community away from the prying eyes of the human governments of the world. Magneto and his Brotherhood have been allowed to set up operations in Genosha with the permission of the United States government and are largely left alone by said government.