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Pele and Maradona - to some, the two best footballers of all time - scored memorable goals and lifted the World Cup there.
It hosted what Fifa has called the 'Game of the Century' - Italy's 4-3 victory over West Germany in the 1970 World Cup semi-finals.
And it will be among the venues for the US-Mexico-Canada World Cup in 2026.
But the Azteca Stadium is currently going through one of its most challenging periods to date.
The NFL game between the Los Angeles Rams and Kansas City Chiefs, which had been scheduled for 19 November, was relocated to LA due to the poor turf conditions.
And the Mexico City ground has gone through several phases of remodelling that have left one of the world's most historic stadiums in serious trouble.
"Today it is not the most important stadium in Mexico - and it should always be," sports analyst Gustavo Velazquez told BBC Mundo.
"We have seen the changes that this stadium has been through and it seems that they have been for the worse, not for the better. It has never been as bad as this."
There are four main reasons why this has happened:
The Azteca Stadium was one of the largest in the world, with the capacity to hold over 100,000 people when it was first built
The most obvious problem is the pitch, which was changed in its entirety in the summer from natural grass to a hybrid pitch.
Those who attended last Saturday's Mexican league game saw the pitch in possibly its worst ever condition.
"The field at Estadio Azteca does not meet NFL standards to be played and its consistency would not meet those standards next Monday," the NFL said in a statement.
Enio Cubillo, an architect from Turf Managers Special (TMS), was in charge of the installation of the new pitch - a job that was completed on 20 July, a day before the Mexican league began.
"There was a change in the dates [of installation] and, since we already had the grass planted in the nursery, we had to make the transfer," Cubillo explained.
By September, it was clear that the pitch had failed to adapt to the hybrid grass and fans were calling it a "paddock".
Both players and coaches have complained about the state of the pitch
"There was unusual rain for Mexico City - although it is known that it rains, it was so much that it caused flooding - and that affects the rootedness of the grass," Cubillo added.
However, stadium analysts say that the Azteca has never had a problem with its grass before. Frequent Azteca visitor Gustavo Velazquez described the current situation as "alarming".
The hybrid grass has had problems embedding itself in the pitch
TMS finalised its contract last month, so Velasquez is certain that the current problems are the responsibility of the new administration.
Cubillo says that his job was only to install the irrigation system for the hybrid pitch and to put sand underneath, but not to perform the current maintenance.
Unlike last season, the Azteca is now home to two teams - so there are games every week instead of every 14 days, as was the way previously.
In addition, the stadium was the venue for a massive concert by Colombian singer Shakira in October - as well as one put on by the TeleHit music channel in early November, which left the pitch damaged.
Shakira's concert added to the problems
The Sports Turf Managers Association (STMA), based in the US, believes part of the problem is the constant wear and tear of the field, in addition to possible drainage problems.
"There has been event after event that has not allowed the field to have a rest," Kim Heck, executive director of STMA, said.
And it is only likely to get worse - the finals of Liga MX will see Azteca's two home teams play back-to-back the first weekend of December.
But the historic stadium also faces other problems of redesign and functionality that, in the opinion of some fans and commentators, have removed the majesty from the work of the great architect, Pedro Ramirez Vazquez.
"100,000 people shouted, and there was born the Azteca" is the famous myth about the creation of the stadium - though various renovations have since reduced its capacity to about 85,000.
The biggest change was made in 2016, when several sections of the stands were redesigned to create VIP roofed areas - criticised by analysts including Velazquez.
"Once teams went out on the field and saw the whole stadium imposed on them in a brutal way - it now seems like they are entering a commercial zone," he said.
"It no longer gives any advantage to the home team."
One of the reforms impacted the visibility from one of the two main stands along the pitch, with metal structures now largely limiting the visibility of the field.
Meanwhile, access to the larger stands with more capacity was cut off, so fans now have to walk around many rows of seats inside to find their place.
The administration of the Azteca Stadium promised last year that there would be "a couple more access points that will meet the capacity of the upper central part of the stadium", after BBC Mundo questioned them about possible security problems in cases of evacuation.
But limited visibility is a problem that remains unresolved.
Meanwhile other problems that have never been properly resolved continue to mount.
The stadium only has space for about 4,000 vehicles in its car park, which is insufficient.
The covered VIP stands reduced the capacity of the stadium, which was no longer among the top places in the world in terms of capacity
And even if a driver finds a space, they still have challenges - there are "caretakers" of vehicles that ask for their own fee to monitor the vehicles of the customers at an additional charge to the regular rate.
"If you do not give them a tip, your car ends up being scratched or blocked," said Velazquez.
In addition, the esplanade of the building - a private space belonging to the Azteca Stadium - is used by informal merchants of T-shirts, food and alcoholic beverages that make access difficult.
"A stadium so big - an architectural project of the 1960s - would have to undergo modifications to adapt to the times, but they have not done it in the right way," added Velazquez.
"Those of us who love the Estadio Azteca and have experienced this metamorphosis do not like it at all."
