The extremist were created by Keith Giffen, Gerard Jones and Bart Sears. In a similar fashion as their enemies, the Champions of Angor (Avenger's DC take) and Squadron Supreme (Marvel's doppelganger JLA) , the original Extremists were molded after the most notable Marvel supervillains from that time: Lord Havok (Dr. Doom), Dr. Diehard (Magneto), Dreamslayer (Dormammu), Gorgon (Dr. Octopus) and Tracer (Sabertooth).
Even if their first appearance is in JLE#15, his paradoxical origin was revealed in Justice league quarterly # 3: five normal humans criminals were trapped in a nuclear explosion and the radiation give them powers. This is a nod on the fact than a lot of Marvel characters have their powers from radiation (From Fantastic Four to Spider-man)
The original Extremists are from the extradimensional world of Angor, same as their enemies, the Champions of Angor. In a bold move, the five more powerful villians united all the supervillians of Angor and take control of their nuclear weapons. However, they were killed in the nuclear event that they started themselves, along with the rest of their world. However, robotic duplicates of the Extremists were created as part of a theme park attraction. The robots, modeled too closely after the violent originals, eventually went berserk. They tracked the surviving Champions (Blue Jay and Silver Sorceress) to Earth, and tried to destroy the planet in the same way they destroyed Angor. They were defeated by the surviving Champions and the heroes of the Justice League Europe . However one of the Extremists, Dreamslayer, revealed not to be a robot, having survived the destruction of his world due to his mystical nature. Instead of being deactivated, he was defeated by the Silver Sorceress and supposly killed. He insted was banished to his home dimension.
The Extremist robots were taken to "Madame Clouseau's" wax museum in Paris. They were later reactivated by Dreamslayer, who was possessing Maxwell Lord at the time. Dreamslayer was again defeated by the Sorceress, though at the cost of her own life. The defeat of Dreamslayer deactivated the other Extremists.
Later, Queen Beatriz of Bialya tries to create an army based on the Extremists' technology, tranforming bialbyans volunteers into cyborgs extremists but her plans were foiled by Captain Atom and Extreme Justice. However the political aftermath of this incident culminated in the disbanding of the UN sanctioned league.
While he was trapped in the Astral Plane, Dreamslayer's services were acquired by the Overmaster. Together, they assembled a new group called the New Extremists. After this, Overmaster imprisoned Dreamslayer in the Astral plane again. The New Extremists became part of Overmaster's Cadre.
Original Extremists Return
The Extremist robots would later be reactivated by Twilight to fight Supergirl and Power Girl. However, after the understanding they were robots, the heroines fighted and destroyed the extremists, leaving only Gorgon "alive".
On Earth-8, the Extremists are a group of villainous outlaws who have refused to comply with a law stating that all metahumans need to register with the government (analogous to the way certain Marvel heroes behaved during the Civil War event).
They battle against the Meta Militia, a group led by Tin Man (a parody of Iron Man), and currently reside in a captured country called Slovekia.
They were encountered by Donna Troy, Jason Todd, " Bob" the Monitor, and Kyle Rayner while the heroes were searching for Ray Palmer.
Lord Havok would later refuse to join Monarch's Army , leading to an encounter where he and Monarch fought, allowing Lord Havok to steal some of Monarch's power for later use.
The original Extremist (less Dr Diehard) made an appearance in the chapter "Shadow of Hawkman" from the Justice League Unlimited Animated series. In the prologue of the story, they were battling Hawkgirl, Green Lantern, Batman and Vixen.