Origin

After the Squadron Supreme took over their universe's Earth in an attempt to create a utopia, they created a device for removing all negative emotions and thoughts from a criminal, called a Behaviour Modifier ("B-Modder"), which would essentially brainwash the subject.  Fearful of this treatment, Mink, Pinball, and Remnant, three supervillains of this world, fled to Earth-616 for sanctuary with the help of Emil Burbank. 

Unknown to them, their enemy Nighthawk had also travelled to Earth-616 around the same time as them, looking for allies to help him overthrow the Squadron, as he found their utopia plans good-hearted, but ethically and morally wrong.  Nighthawk was told by Professor Imam, the one who sent him to Earth-616, that he would automatically return once he found allies.  After the Avengers, Fantastic Four, and X-Men all kindly rejected Nighthawk's plea for allies, Nighthawk heard about Mink, Pinball, and Remnant going on a crime spree to establish themselves in Earth-616.  He managed to track them down, and get into a fight with them, before they explained why they were on Earth-616.  Nighthawk then suggested that they work with him to oppose the Squadron, and the trio of criminals agreed. 

Creation

Team Evolution

After the initial members, the team quickly expanded, with Nighthawk finding new superhumans on Earth-712 who hadn't publicly revealed their powers.  Each of these superhumans infiltrated the Squadron as double agents.  From here, the schematics of the B-Modder were stolen, and used to undo the conditioning of the former Institute of Evil members whom had been B-Modded into joining the Squadron. 

Final Lineup

Major Story Arcs

Opposing the Squadron

With Remnant, Mink, and Pinball now his allies, Nighthawk set about gathering more allies.  Using a magic crystal which Professor Imam had given him, Nighthawk managed to find several new allies - Redstone, Haywire, Thermite, Inertia, and Moonglow, who all agreed to infiltrate the Squadron as double agents.  The Squadron Supreme suspected nothing when they were approached by these members and asked to join, and after passing several tests, happily let them join. 

Now that they had infiltrated the Squadron, Moonglow carried out Nighthawk's plan: by gaining the schematics to a B-Modder, he hoped to find some way to undo B-Modding, which he could then use on the members of the Institute of Evil who had been forcefully B-Modded into the Squadron Supreme.  Although Moonglow was successful, she was spotted by Ape X, who subsequently went catatonic as a result of conflicting B-Modded orders (she wasn't allow to betray or report any Squadron members, which Moonglow was, yet was supposed to report all thefts, which Moonglow was doing, thus creating a paradox). 

Whilst his Redeemers had been infiltrating the Squadron, Nighthawk and the rest of his team had meanwhile been busily training for the upcoming battle (although Nighthawk didn't really want a fight).  The Redeemers also gained a member in Black Archer, the former Golden Archer of the Squadron Supreme, who had been thrown out for abusing the B-Modder.  Nighthawk gave the B-Modder schematics which Moonglow had recovered to Emil Burbank, as they had a mutual interest in overthrowing the Squadron.  Within a week, Emil found a way to undo the B-Modding. 

Over the course of several weeks, the double agents within the Squadron led the former members of the Institute of Evil to a decrepit house, where Nighthawk was keeping the machine that would undo the B-Modding.  Although they managed to undo the B-Modding of the former Institute of Evil members (which by this point, had been cut down to Shape, Foxfire, and Lamprey), there were problems.  The treatment didn't seem to have a very strong effect on Shape, due to his low intellect.  Although it worked on Foxfire, she had started to grow genuinely attached to the Squadron, as she had fallen in love with Doctor Spectrum.  And when the team brought Lamprey over for the treatment, Blue Eagle spotted them and followed.  This left Nighthawk with two options: either B-Mod him into forgetting that he had seen them, or kill him.  Nighthawk went with the B-Modding option, seeing it as the lesser of two evils, but knew that he was still compromising his morals, and everything he had worked for in opposing the Squadron. 

The Final Fight

After the Squadron delivered a speech to the nation as to what they had achieved and how everything had ultimately worked out, Nighthawk, Golden Archer, Mink, Pinball, and Remnant confronted them, with Nighthawk planning to explain to the Squadron where they had gone wrong and how they had failed in their goal.  As Hyperion pointed out to Nighthawk that he hardly had the force to stop them, Nighthawk revealed his trump card - that more than half of the members of the Squadron Supreme were now working for him. 

In an attempt to stop things from escalating to violence, Doctor Spectrum used his Power Prism to create improvised handcuffs around all of the fake Squadron members' hands.  Unfortunately for both teams, this merely provoked Inertia into attacking back, which soon erupted into a fight.  The fight ended up being bloody and violent, with many deaths on both sides.  It was only after Foxfire killed Nighthawk, who was killed herself by Mink a moment later, that both teams stood down, and ended things.  The casualties are as follows:

To show her loyalty to the Squadron, Foxfire used her powers to give Nighthawk a fatal heart attack. 

Thermite was accidentally kicked by an out-of-control Whizzer, causing his power pack to flare up and encase him (Thermite) in a giant block of ice. 

After Lamprey drained the power out of Blue Eagle's wings, Blue Eagle managed to glide and land on Pinball.  This killed both of them instantly. 

Doctor Spectrum used his Power Prism to overload Lamprey's energy absorbing abilities, causing him to explode. 

Foxfire was stabbed by Mink as revenge for killing Nighthawk, whom she had a crush on. 

Although he wasn't killed, when Black Archer shot Doctor Spectrum's Power Prism, the Prism shattered into fragments which became embedded in Spectrum's skin, turning him chalk-white unless he was using his powers. 

After the fight, the remaining members of the Redeemers folded into the Squadron Supreme. 

Alternate Realities

There have been no alternate versions of the Redeemers seen so far, although alternate versions of individual members have been seen.