The Elite Four is a Trainer Class and title given to four Trainers that qualify as being the best Trainers in their respective regions, with only the Pokémon Champion above their skill level. There are currently 7 sets of Elite Four members and 1 Champion, corresponding to the number of Generations that the main series games have been through (although Kanto and Johto share their respective Elite Four location, the Indigo Plateau, which, technically, is in the Kanto region).
In order to challenge the Elite Four, a Trainer must first acquire a total of 8 Badges (16 in Pokémon Gold and Silver and HeartGold and SoulSilver, but you first fight them with 8). Upon battling them, the challenger must face all of them consecutively. In Generations I-IV, the members of the Elite Four are battled in a set order. Since Generation V, they can be fought in any order. Once defeated, a Trainer can battle the regional Pokémon Champion for their title. However, in every region, if the player character is defeated at any point, then they must re-battle all members of the Elite Four.
In Galar, there are no Elite Four. Because of this, the Galar Pokémon League only have the Champion Cup, where the player character only battle the rivals, three of the eight Gym leaders, in the Semi-Finals and Finals receptively and battle the Champion in championship match.
In the Pokémon anime, Ash and his friends infrequently meet Elite Four members, who then impart them with battle strategies.
In Kanto, Ash has met the entire original Elite Four roster:
Bruno was the first Elite Four member to appear in the anime (excluding Koga, who was later promoted to be one in Generation II), in To Master the Onixpected.
Lorelei appeared in The Mandarin Island Miss Match, but she is named "Prima" in the English dub.
Lance debuted in Talkin' 'Bout an Evolution, where he was mentioned to be the Champion rather than a regular member of the Elite Four. He is referred to as a member of the Elite Four in Flash of the Titans!.
Agatha appeared in The Scheme Team, where she was acting as a temporary Gym Leader for the Viridian Gym.
Koga, though not an Elite Four member, debuted in The Ninja Poké-Showdown, where he had a Gym battle against Ash.
Drake appeared in Vanity Affair, where he invited Ash and his friends to his boat, where he had a battle with Ash.
In Sinnoh, Ash has also met the entire Elite Four roster:
Lucian debuted in An Elite Meet and Greet!, where he had a battle with Dawn, using his Bronzong against her Buizel.
Aaron debuted in A Trainer and Child Reunion!, where he was seen training to challenge Cynthia.
Flint debuted in Flint Sparks the Fire!, where he had a battle with Ash, using his Infernape against his Buizel, Infernape, and Pikachu.
Bertha appeared in An Elite Coverup!, where she taught Ash and Dawn how observation skills can be useful in battles and Pokémon Contests.
In Unova, Ash has also met only one Elite Four member:
Caitlin debuted in Jostling for the Junior Cup!, where she faced off against Cynthia during an exhibition match of the Pokémon World Tournament Junior Cup.
In Kalos, Ash has met Malva and Wikstrom. One other Elite Four member has appeared as well:
Siebold appeared in Mega Evolution Special I, where he used his Mega Blastoise to battle Alain and his Mega Charizard X.
Wikstrom first appeared in a cameo in Diancie and the Cocoon of Destruction, in which he was seen battling Diantha, using his Mega Scizor against her Mega Gardevoir. He made his main series debut in Searching for Chivalry!, in which Ash met him for the first time when he visited the Castle of Chivalry.
Malva debuted in Cloudy Fate, Bright Future! in a video transmission. Ash didn't meet her until A League of His Own!, where he was interviewed by her.
In Alola, Ash has met the entire Elite Four rosters from both the Sun and Moon and Ultra Sun and Ultra Moon paired versions, though none of them presented themselves as such, because the Alola League was not established until The Dealer of Destruction! in the anime:
Hala debuted in To Top a Totem!, where he led Ash to Verdant Cavern so he could start his island challenge.
Olivia debuted in The Island Whisperer!, where she took Ash and his classmates to Akala Island and began hosting them during their stay there.
Acerola debuted in Why Not Give Me a Z-Ring Sometime?, though Ash didn't meet her until the next episode, where she assisted him in his first battle against Nanu.
Molayne debuted in Showering the World with Love!, where he showed Ash and his classmates around the Hokulani Observatory.
Kahili debuted in Keeping Your Eyes on the Ball!, where she took Ash and his classmates to a Pokémon Golf course and taught them the sport.
It has been stated by Lucian in An Elite Meet and Greet! that when a Trainer wins their respective region's League Conference, they can participate in the Champion League, fighting the members of that region's Elite Four, and then the Champion as well. It has also been shown that an Elite Four member can challenge the Champion and obtain the title from them in battle.
Trivia
With Ritchie currently being the only exception, members of a region's Elite Four typically only specialize in one specific type of Pokémon (much like gym leaders).
The Kanto, Hoenn, and Unova Elite Four are similar, however, at least one type needs to be changed in order for them to be the same.
The Unova Elite Four is the first one that allows the player to choose the order in which the Elite Four is battled. The Kalos and Alola Elite Four also shares this trait.
The Kalos Elite Four are the first Elite Four who's Pokémon do not go up levels when the player returns to the Pokémon league for their first rematch, in fact they stay at the same levels as the first time the player fought them for all rematches.
There has never been a Champion or Elite Four-member specializing Normal, Fairy, Electric or Grass Pokémon.
Bruno has the most Elite Four appearances - Kanto's second and Johto's third places.
Pokémon: Let's Go, Pikachu! and Let's Go, Eevee! are the only games to date in which the player can change their Pokémon party between Elite Four matches, due to the presence of the Pokémon Box in the player's Bag.
Galar is the only region that does not have the Elite Four.
There are more Ghost-Type specialist Elite Four members than any other type, with a total of 4.
Siebold is the only Elite Four member that specializes in Water-type Pokémon.
According to designer Yusuke Ohmura, the Unova Elite Four was designed based on the theme of "black and white". This explains why Shauntel and Grimsley sport black clothing, whereas Caitlin and Marshal wear white garments.
This concept is also accentuated through the types these two different pairs use; Ghost and Dark-types are considered as vague and mysterious, while Psychic and Fighting-types are heralded as straight and enlightened.
