It was founded in 1992, when Antonio Peña broke away from Consejo Mundial de Lucha Libre (CMLL) to set up his own promotion to have more creative freedom.

[citation needed] The promotion became known for signing top talent, such as El Hijo del Santo, Octagón, Blue Panther, the Casas brothers (Negro Casas and Heavy Metal), Los Gringos Locos, Cien Caras, Konnan, and Perro Aguayo.

[citation needed] The rising popularity of AAA caused rival promotion Universal Wrestling Association to go out of business.

[citation needed] Peña would quickly sign up top draws, including El Canek, Dos Caras and Los Villanos.

[7] Weeks after the show, Art Barr (a key member of Los Gringos Locos) died while visiting his family.

[citation needed] Talent such as Rey Misterio, Jr., Psicosis, La Parka, and Juventud Guerrera, would also depart to WCW in 1996, as well as Konnan's short-lived Promo Azteca promotion.

In early 1997, AAA established a working agreement with the World Wrestling Federation (WWF), with several luchadores appearing in the 1997 Royal Rumble.

Through the relationship, AAA sent the luchadores Juventud Guerrera, Héctor Garza, Abismo Negro, Heavy Metal, and Mr. Águila to TNA to compete in the America's X-Cup Tournament as a contingent known as Team Mexico.

[13] On January 12, 2014, it was announced that, with the backing of Mark Burnett, AAA would co-produce a show for the American El Rey Network in the second half of the year.

[citation needed] On February 1, 2019, AAA announced the end of their relationship with Televisa after 27 years, with the promotion's programming moving to the Multimedios television station.

[20] On April 4, 2019, AAA announced its first event to be held in the United States, Invading NY, would take place at Madison Square Garden on September 15, 2019.

[21] The promotion also announced that would hold a second event in the US titled Invading Los Angeles, at The Forum in Inglewood, California on October 13, 2019.

[22] On August 16, 2019, it was reported by Pro Wrestling Insider that Invading NY was moved to Hulu Theater due to poor ticket sales.

[citation needed] The following April, a tournament called Lucha Fighters was created consisting of 12 luchadores and 8 luchadoras.

[citation needed] In 1997, AAA partnered with World Wrestling Entertainment (WWE) to bring in a number of luchadores for the Royal Rumble event and its namesake match.