Smith and Carlos' black power salute captures the mood of the world
Being more than 2,300 metres above sea level, Mexico City with its searing temperatures was far from ideal for strenuous competition. But this was not the only place where things were reaching boiling point. All over the world people were taking to the streets in protest.
In the United States thousands of people demonstrated against their country's involvement in the Vietnam War. In France student riots almost toppled the government. In Czechoslovakia the situation was even more serious as Soviet troops and tanks rolled into Prague to crush anti-Russian uprisings.
Then, in Mexico City itself, just 10 days before the opening ceremony troops opened fire on demonstrators in the Plaza de las Tres Culturas, killing 250 people and injuring hundreds more.
The International Olympic Committee dismissed the incident as an "internal affair" and continued on its preparations for the Games.
If the IOC were happy to turn a blind eye to the protest on the streets of Mexico , they were forced to respond when two American athletes staged their own demonstration under the organisers' noses in the Olympic Stadium.
Tommie Smith and John Carlos won gold and bronze in the 200 metres, with Smith breaking Carlos' world record. But if the race left the spectators roaring their approval, the medal ceremony had the powers that be baying for blood.
The two black sprinters shunned the American national anthem and stood barefoot, heads bowed, with their fists clenched in protest against the US government's treatment of black Americans.
It remains one of the most vivid Olympic images - a picture once seen, never forgotten. It was a courageous, non-violent protest, benign but impassioned dissent. They meant to bring further attention to civil rights issues, to give pride to African-Americans, and they succeeded.
But the reaction was as swift as it was negative. In the US there was outrage from many white Americans. People saw heads bowed as disrespectful towards the American flag. They mistakenly saw the clenched fists as supportive of the Black Panthers.
The Associated Press report described them "in a Nazi-like salute". Chicago columnist Brent Musburger called them "black-skinned storm troopers".
The outspoken Carlos made the kind of comments that only inflamed the establishment. After the ceremony he said: "We're sort of show horses out there for the white people. They give us peanuts, pat us on the back and say, 'Boy, you did fine.'"
The pair were immediately suspended and evicted from the Olympic Village. But they still had their medals and they had made their point.
The rarefied atmosphere of Mexico City also helped another black American athlete make his mark on Olympic history.
Bob Beamon leapt into the record books with his incredible long jump of 8.90 metres - a world best that stood for 23 years.
Many new records were set in the short distance sprint events due to the altitude, but the Games were a nightmare were a nightmare for endurance competitors who had failed to adjust to it.
In the 10,000m Australia 's world record holder Ron Clarke, who had lit the torch at the 1956 Olympics in Melbourne , could only finish sixth and, on crossing the line, he collapsed and was unconscious for 10 minutes. Thankfully, he recovered.
These Games were also noteworthy because they included the first athlete to be disqualified for taking drugs. Sweden 's Hans-Gunnar Liljenwall was banned from the modern pentathlon after testing positive for excessive alcohol.
Date Games held: October 12-27
Number of nations represented: 112
Number of competitors: 5,243 (768 women)
Number of medal events: 172