The Brotherhood of Mutants was a group of trouble-making, mutant teenagers. It was brought together by Mystique (secretly working for Magneto), the core group consisted of Avalanche, Toad, Blob, and Quicksilver.
The Brotherhood were created by Mystique and opposed to the X-Men's ideals in favor of personal power. The Brotherhood also attend the same school with the X-Men at Bayville High and occasionally had few arguments with their adversaries. Due to the shifting loyalties of Mystique and long periods of absence from Magneto, these four teens were often left without any guidance.
Each member had faced the X-Men's most powerful member, Superman, and were easily beaten. Although the Brotherhood had a grudge on Superman, most especially the egotistical Quicksilver, the other three members shown some respects for the Man of Steel's heroism.
Although the Brotherhood follows Magneto's beliefs of mutant supremacy, they were not given the full details of their master's plans and intentions. At Asteroid M, the Brotherhood (except for Quicksilver) were never told of Magneto's attempted genocide to wipe out most if not all of Earth's human population by bombarding the planet with a passing meteor shower. This revelation caused Avalanche to betray Magneto and helped Superman and the X-Men in foiling his plot, and ultimately leaving the Brotherhood out of disgust and joining the X-Men.
Following the events on Asteroid M, Quicksilver briefly became the de-facto leader of the Brotherhood, which had decided to work on their own without Magneto's guidance. The Brotherhood later gatecrashed Bayville High's pep rally and threatened to expose mutantkind to the world. Fortunately, Superman and the X-Men stopped their rampage and every witness attending the rally had their memories erased by Professor Xavier. Quicksilver's leadership was then taken over by Doctor Doom's daughter, Siryn, and seeing to directly battle the X-Men and gaining Superman's affections.
Under Siryn, the Brotherhood had briefly included the Scarlet Witch (Wanda Maximoff) as a powerful magical deterrent against Superman. However, the Scarlet Witch learned of her manipulations by Siryn and eventually joined the X-Men.
By the time mutants were exposed to the public due to Magneto and Doom's machinations, Toad and Blob followed Avalanche's example and altogether quit the Brotherhood. In time, Toad and Blob would also eventually enroll in the Xavier Institute (though it was partly factored to the loss of their home, the Brotherhood of Bayville Boarding House, during General Zod's rampage).