The Extremists were an homage to several Marvel Comic villains akin to how the Champions of Angor were homages to the Avengers. The original team were from the planet Angor in another dimension.
They were destroyed along with all other natives of Angor (minus the Champions of Angor) in a nuclear holocaust they created. However, before this, a theme park made robot copies of the Extremists for a ride. The robots were too accurate. They went on rampage and tracked down remaining members of the Champions of Angor and tried to destroy them. It turned out Dreamslayer was the real deal and was the only one of the real Extremists to survive. The Heroes (with the help of Mitch Wacky, the owner of the park) turned off the robots, while Silver Sorceress defeated Dreamslayer.
The robots were sent to "Madame Clouseau's" (spoof of Madame Tussauds) in London. Maxwell Lord (possessed by Dreamslayer) restored the robots, during the Breakdowns storyline. Despite dying from being shot by an arrow, Silver Sorceress managed to defeat Dreamslayer again and (since his magic was powering the robots) the robots were stopped in the process. Queen Beatriz, later, tried to create an army she based on the team's armor, only to be stopped by Captain Atom and Extreme Justice.
Dreamslayer, trapped in the astral plane, was contacted by an villain called The Overmaster. The duo created a villain team call the New Extremists. This was intended to be a "lead-up" for the Judgement Day storyline. After the Overmaster got what he wanted, he sent Dreamslayer back to the astral plane, but the New Extremists are assumed to still be at large.
In Supergirl, an villain called Twilight activated Extremists robots, but the titular character stopped them. How the robots were rebuilt hasn't been revealed. This version of the team appeared in the JLA/Avengers crossover.
After Infinite Crisis, on Earth-8, the Extremists are revamped as a group of villains that refused to comply with a law stating superhumans must register themselves to the government. In Countdown # 29, Donna Troy, "Bob" the Monitor, Kyle Rayner and Jason Todd meet this version of the team. The Extremists capture the heroes only to be interrupted by the arrival of Bob's brother, Monarch and Forerunner. In the confusion, the heroes escaped. The Extremists refused to join Monarch's army and Lord Havok tried to kill Monarch. Jason killed Barracuda. The team had a mini-series. In issue 1, it's revealed they are superhumans that refused to submit themselves to the goverment's Megahuman Act (a parody of Marvel's Civil War). They battled against the Mega-Militia, led by Tin Man (Iron Man spoof). The team based themselves in a country called Slovekia. After refusing Monarch, Monarch sent forces to attack Tracer and places important to the team. In Countdown to Final Crisis # 13, Superman-Prime rips open Monarch's suit and, as a result, destroys Earth-51, while Lord Havok (using some power he stole from Monarch) teleported his team to a hidden moon based.
- Lord Havok (Doctor Doom)- An arrogant villain with hi-tech armor. He is the team leader.
- Dreamslayer (Dormammu)- A sorcerer (and a very powerful one), who is possibly a demon. In Extremists, he is (in fact) a she. She has her own religion (even has followers).
- Gorgon (Doctor Octopus)- An overweight man, who has tentacles coming out his head and two metal claws. In Extremists, he can turn people into "Extremist form",which is shorter than his original version.
- Tracer (Sabbertooth, but the Earth-8 version is similar to Wolverine)- Feral and has blades attached to his arms. He also has superhuman senses (hence the name).
- Doctor Diehard (Magento)- Magnetic manipulation. He wears a red cape and a helmet that exposes his face. The Earth-8 version has a school for "Zen-Men" (Professor X homage).
- Carny (Arcade)- Has a robot copy that appears in Extremist Vector storyline. His first "real" appearance is in Lord Havok and the Extremists # 1, where Hovak killed him for not serving him.
- Brute- A not-very-smart powerhouse
- Cloudburst- A man with weather control
- Death Angel- She has (possibly) poisoned claws.
- Gunshot- He is a " taciturn weapon-user." Enough said.
- Meanstreak- Able to shoot energy bolts. She is very vicious.
- Earth-8 versions of Lord Havok, Dreamslayer, Doctor Diehard, Gorgon, Tracer and Carny.
- Barracuda (Namor)- A fish-like being.