Original run (2002–2005)
At Unforgiven on September 22, 2002, Triple H defended the World Heavyweight Championship against Rob Van Dam. During the match, Ric Flair, who had been verbally mocked by Triple H in the locker room earlier in the night following his Intercontinental Championship loss to Chris Jericho, came down to the ring and grabbed the sledgehammer from Triple H and teased hitting him before hitting Van Dam instead, allowing Triple H to get the win. From that point on, Flair accompanied Triple H to the ring as his manager. Shortly thereafter, Batista moved from SmackDown! to Raw and Flair also began accompanying him to the ring as a manager and mentor while continuing to second Triple H. On the January 20, 2003 episode of Raw, Randy Orton, who had been out of action due to a shoulder injury, returned and joined Triple H, Flair and Batista in attacking Scott Steiner to complete the group. Two weeks later, the group officially got its name when Triple H, after the group jumped Tommy Dreamer, spoke about how the four men were examples of professional wrestling's evolution from the past (Flair) to the present (himself) to the future (Batista and Orton). During the group's early stages, however, Batista was out of action for nearly eight months due to a triceps tear.
At Bad Blood on June 15, Flair defeated Shawn Michaels in a singles match after Orton struck Michaels with a chair. Later that night, Triple H retained his World Heavyweight Championship against Kevin Nash in a Hell in a Cell match. On the June 23 episode of Raw, Triple H successfully defended the title against Kane in a match with a "Title vs. Mask" stipulation, forcing Kane to unmask. At Unforgiven on September 21, Orton defeated Michaels to help establish his "Legend Killer" gimmick. Later that night, Triple H lost the World Heavyweight Championship to Goldberg. The following week on Raw, Triple H issued a $100,000 bounty to anybody who could take out Goldberg. On the October 20 episode of Raw, Batista made his return from injury during Goldberg's World Heavyweight Championship defense against Michaels, attacking Goldberg and finishing by stomping on a steel chair with Goldberg's ankle sandwiched in it to claim the bounty. At Survivor Series on November 16, Orton participated in the Team Bischoff versus Team Austin elimination tag team match, in which he was the sole survivor. Later that night, Triple H failed to regain the World Heavyweight Championship from Goldberg.
At the height of Evolution's power, the group controlled all of the male-based championships of Raw after Armageddon on December 14. Batista and Flair won the World Tag Team Championship in a tag team turmoil match, Orton captured the Intercontinental Championship from Rob Van Dam, and Triple H regained the World Heavyweight Championship from Goldberg in a triple threat match also involving Kane.
On January 25, 2004 at Royal Rumble, Flair and Batista successfully defended the World Tag Team Championship against the Dudley Boyz (Bubba Ray Dudley and D-Von Dudley) in a tables match, and World Heavyweight Champion Triple H fought Shawn Michaels to a no contest in a Last Man Standing match, thus retaining the championship. On the February 16 episode of Raw, Flair and Batista lost the World Tag Team Championship to Booker T and Van Dam. At WrestleMania XX on March 14, Evolution defeated the Rock 'n' Sock Connection (The Rock and Mick Foley) in a 3-on-2 handicap match. Later that night, Triple H lost the World Heavyweight Championship to Chris Benoit in a triple threat match also involving Michaels when he tapped out to the Crippler Crossface. On the March 22 episode of Raw, Flair and Batista defeated Booker T and Van Dam to regain the World Tag Team Championship. At Backlash on April 18, Flair lost to Shelton Benjamin. Later that night, Orton successfully defended the Intercontinental Championship against Foley in a hardcore match, while Triple H failed to regain the title in a triple threat rematch after Benoit forced Michaels to submit with the Sharpshooter. While still World Heavyweight Champion, Benoit teamed with Edge to win the World Tag Team Championship from Flair and Batista on the April 19 episode of Raw. At Bad Blood on June 13, Triple H defeated Michaels in a Hell in a Cell match to end their feud.
In mid-2004, Eugene befriended Triple H, who seemingly reciprocated the friendship. At Vengeance on July 11, it was revealed that Triple H had used Eugene to try and regain the World Heavyweight Championship from Benoit, but he was unsuccessful after Eugene inadvertently hit him with a chair. On the same night, Edge defeated Orton to end his seven-month long Intercontinental Championship reign. Triple H received one final shot at the World Heavyweight Championship on the July 26 episode of Raw in a 60-minute Iron Man match. Earlier that night, Orton won a battle royal to determine the number one contender for the title at SummerSlam, teasing a title match between him and Triple H. However, Eugene interfered in the Iron Man match and helped Benoit take the lead and retain the title in the final seconds, making the main event of SummerSlam a title match between Benoit and Orton. At SummerSlam on August 15, Orton pinned Benoit to become the new World Heavyweight Champion and the youngest world champion in WWE history to date.
The next night on Raw, after successfully defending the title in a rematch against Benoit, Orton was kicked out of Evolution. Batista hoisted Orton on to his shoulders in what appeared to be a celebration, but following the thumbs down from Triple H, the group proceeded to attack Orton. On the August 23 episode of Raw, Triple H demanded that Orton "make the right decision" and give him the World Heavyweight Championship belt, but Orton refused and spat in his face. At Unforgiven on September 12, Triple H defeated Orton to regain the World Heavyweight Championship with help from Flair, Batista and Jonathan Coachman. At Survivor Series on November 14, Triple H, Batista, Gene Snitsky and Edge lost to Orton, Maven, Chris Jericho and Benoit in a Survivor Series match where the winning team would gain control of Raw over the following month. On the December 6 episode of Raw, the championship was vacated when a triple threat match the previous week with Triple H, Edge and Benoit ended in a double pin (Edge tapped out to Benoit's Crippler Crossface while he simultaneously had Benoit pinned to the ground), and the title was to be decided in an Elimination Chamber match at New Year's Revolution on January 9, 2005.
In the Elimination Chamber match at New Year's Revolution, Batista, Orton and Triple H were the last three remaining in the match. Orton eliminated Batista with an RKO and Triple H pinned Orton with Batista's help to win the title. On the following night's Raw, Orton defeated Batista to gain a title shot at the Royal Rumble on January 30. Triple H suggested that Batista not enter the Royal Rumble match, wanting the group to focus on Triple H retaining the title. Batista declined, entered the Royal Rumble match at number 28 and won by last eliminating John Cena. Earlier that night, Triple H defeated Orton to retain the title, ending their feud.
Following Batista's Royal Rumble win, Triple H tried to persuade him to challenge WWE Champion John "Bradshaw" Layfield (JBL) of SmackDown! rather than challenge him for his World Heavyweight Championship. This involved Triple H plotting a feud between JBL and Batista, showing JBL badmouthing Batista in an interview and staging an attack on Batista with a limousine designed to look like JBL's, but Batista became aware of the scheme while sneakily eavesdropping on fellow Evolution members. On the February 21 episode of Raw, during the brand contract signing ceremony, Batista chose to remain on Raw, powerbombing Triple H through a table and leaving the faction, turning face in the process. At WrestleMania 21 on April 3, Batista defeated Triple H to win the World Heavyweight Championship. He successfully defended the title against Triple H at Backlash on May 1 and in a Hell in a Cell match at Vengeance on June 26. On the June 30 episode of SmackDown!, Batista was drafted to SmackDown! as the last pick in the 2005 WWE draft lottery, effectively ending Triple H's pursuits for the title.
After Vengeance, Triple H took some time off due to neck issues, not being seen on WWE television for four months. In the interim, Flair turned face and won the Intercontinental Championship from Carlito at Unforgiven on September 18. Triple H returned to action at the "WWE Homecoming" episode of Raw on October 3, teaming with Flair to defeat Carlito and Chris Masters. After the match, Triple H betrayed Flair and attacked him with a sledgehammer, marking the definitive end of Evolution. Flair then defeated Triple H in a steel cage match to retain the Intercontinental Championship at Taboo Tuesday on November 1. Triple H defeated Flair in a Last Man Standing match at Survivor Series on November 27.