It was during the 200 metres victory ceremony at the 1968 Olympics. Smith had won in world-record time; Carlos had captured the bronze.
As they stood on the victory platform and the US anthem began, they bowed their heads, and, each wearing a black glove, raised a clenched fist in a black power salute. Australia's Peter Norman, who won silver, wore an Olympic Project for Human Rights badge in support of the pair.
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 International Olympic Committee demanded the US Olympic Committee ban them from the Games, but it refused. The next day the IOC said if the sprinters were not banned, the entire US track and field team would be barred from further competition. The USOC caved in.
Smith and Carlos were withdrawn from the relays and expelled from the Olympic Village. When they returned home, Smith and Carlos were ostracised. Jobs became scarce. They received death threats and their homes were attacked.
"One rock came through our front window into our living room, where we had the crib," Smith said. "It seemed like everybody hated me. I had no food. My baby was hungry. My wife had no dresses."
Even today, there are those who remain angry and full of hatred.
"There are still threats," Carlos said. "I was never concerned about those punks. I just let them know it will be remembered, that life doesn't stop when you leave this planet."
After graduating, Smith was given an honourable discharge from army service for "un-American activities" That probably did him a huge favour, since the Vietnam war was raging and the body count growing.
"I was going to 'Nam," Smith said. "I could see myself in rice paddies. I believe there's a God. Sixty-eight had its downfall, but it had its protection for me. I might not be alive."
Carlos had two brothers serving, but after his protest both were immediately discharged.
Smith borrowed money to complete his education and get his teaching qualification. He tried gridiron for a few years with the Cincinnati Bengals, then finally got a job as a track coach in Ohio. In 1978 he moved to Santa Monica College, where he has been a social science and health teacher, and coaches track and field.
Carlos had an even more trying time, working as a security guard and bouncer, among other jobs.
"I'd get minimum wage and then go to Vegas and roll the dice to get it up to something to feed my family," he said. "We had to chop up furniture, the kids' beds, to stay warm."
Looking back, the first thing that comes to him is basic.
"That I survived," he said. "That I still have any sanity.
"My first wife is deceased as a result. She took her life because she couldn't deal with the pressure from the results of Mexico."
