Pressure? Every Olympian feels that. Try being 19, in your first Olympics and one routine away from the biggest prize in your sport: a gold medal that only 14 women have ever won, yet one everyone in the arena expects you to take home as surely as you got out of bed that morning. Knowing the lead was hers to lose, Simone Biles stepped onto the platform at the Rio Olympic Arena on Aug. 11 for the floor exercise, the final event in the women’s gymnastics individual all-around and the only one that stood between her and gold.

“I told her to do it for herself and do it from joy,” says Aimee Boorman, who has coached Biles since she was 8. “I didn’t even want her to think about what she had to do. I just wanted it to flow.” And it did. Biles, the first woman to win three consecutive world titles, whipped off a display of soaring, spectacular tumbling–including a maneuver so distinctive, it bears her name–and won gold by an almost unheard-of margin. And then, finally, the giggly teenager from Spring, Texas, allowed the pressure to melt and the tears to pour out. “Every emotion hit me at once, so I was just kind of a train wreck,” Biles said.

Hours later and a 15-minute walk away, another Olympian was chasing history. Michael Phelps was competing in his fifth Games, not his first, but the pressure on him was no less. The phenom who made the U.S. swim team in 2000 at 15, emerged as a force in 2004, crushed all comers in 2008 and then nearly wilted under the superhuman expectations in 2012 was hell-bent on writing a storybook ending to the most decorated Olympic career of all time. And so in what he told everyone would be his final Games, Phelps, 31, threw off his 10-ton weight and blitzed past rivals in the 200-m individual medley by practically the same margin as Biles’ for her gold, which in his case wasn’t two points but nearly two seconds. With it, Phelps became the first swimmer to win the same event in four straight Games–setting yet another record at an Olympics full of them.

A good number of those marks were claimed by Phelps’ fellow Marylander Katie Ledecky, who racked up four gold medals and a silver through steely determination and unparalleled range. And another was set by a man, like Phelps, who was committed to making his curtain call as impressive as the acts that came before it.

When Jamaica’s Usain Bolt won the 100 m on Aug. 14 for an unprecedented third consecutive Olympics, he did more than burnish his title as the world’s fastest man. Bolt’s joyous gallop to victory confirmed that the 2016 Rio Olympics would be remembered as an ebullient celebration of greatness, 16 days filled with joy, drama and hope. For all the worry over what would go wrong in Rio, the spectacular achievements of these four athletes in the face of unimaginable expectations–and the countless triumphs of many hundreds of others–compelled us with all that went right.

Ledecky may not have been a familiar name before the 2012 Olympics, but she was well known by the men on the U.S. swim team. At the squad’s training camp ahead of London, Ledecky, then only 15, was nipping at some of the men’s times–and eager to beat them. “I talked to the coach, and he was like, ‘Yeah, sometimes this girl–I need to separate them, so the environment wouldn’t get as competitive,'” says Bruce Gemmell, who started training Ledecky after London.

Four years later, Ledecky is still the youngest member of the U.S. swim team and is even more ferocious in the pool. In Rio, she laid waste to her own world record in the 400-m freestyle and broke another one (hers again) in the 800-m freestyle. As if that weren’t enough, she won the sprintlike 200-m freestyle too. “It’s just unbelievable that someone can swim the sprint and distance events and be dominant all the way through,” says Dara Torres, a 12-time Olympic medalist. “I’ve never seen that before. I’ve never heard of that before.”

Should anyone break Phelps’ Olympic record of 23 gold medals (and it’s a huge if, given that the haul is more than some 100 entire nations have ever won), Ledecky is a fair bet. Phelps says as much himself. “What she is doing in the sport is ridiculous, it’s insane,” he said. “She just gets in the water and pretty much gives the world record a scare.”

Phelps set out to do the same thing in Rio. He spun out after London, where that 10-ton weight proved too much, and racked up a DUI arrest in 2014 before entering rehab. These Games, his first as a father, would be his chance to make it right, to end his career in the manner it deserved. And so the greatest swimmer of our time–likely the greatest of all time–swam as if he had nothing to lose. He demolished younger rivals in the 200-m butterfly and that medley, and led the U.S. to three relay golds with a visceral sense of joy that wasn’t there in his four previous Olympics. Even the one race he didn’t win was a victory of sorts. After Singapore’s Joseph Schooling out-touched Phelps for gold in the 100-m butterfly, a 2008 photo of them together, when Schooling was 13, went viral. “I wanted to be like him,” Schooling says. “I don’t think I would be at this point without Michael.”

Phelps relished that everything came full circle in Rio. “I was a little kid with a dream, which turned into a couple of medals and a pretty good couple years of swimming,” he said. “I had a blast.”

“Bolt! Bolt! Bolt!” The chants were deafening inside the packed Olympic Stadium before the world’s greatest sprinter defended his crown. During his warm-up, while his opponents were lingering at the start line, Bolt jogged down the track, turned around and held his arms up, a royal bathing in the adulation.

Meanwhile, Bolt’s chief rival, American Justin Gatlin, was met with lusty boos. Sure, Gatlin still was paying the price for a decade-old doping violation, which led to a four-year suspension in the prime of his career. But these fans knew that Gatlin, who fell just 0.01 seconds shy of dethroning Bolt at the 2015 world championships, had a real shot. And they didn’t want anyone, especially this man, spoiling a coronation.

And then the gun went off, and Bolt erased all doubt. He lagged early. “I kind of felt dead at the start,” Bolt said. But he quickly found the gear that only he has, bounding past Gatlin to claim his third consecutive gold in the fastest 10 seconds in sports–and set one more record in Rio. And then, for the third Olympics in a row, a victorious Bolt worked the crowd better than a politician on a parade line. He hoisted a stuffed Olympic mascot, mugged for selfies and crouched low and flexed in his trademark lightning-bolt pose. A track meet had given way to a rock concert.

Pressure? Bolt has always performed best on the biggest stages. And none are bigger than the Olympics, where his 100-m win made it seven straight golds, in seven races, over three Games. There won’t be a fourth. Like Phelps, Bolt insists that Rio will be his last Olympics. The void he leaves will be hard for anyone to fill. “Hopefully, younger athletes can understand that the sport is looking for people who are full of energy,” Bolt says. “That’s what gets them going, the hype. They like to be a part of the competition. Not just watching it.”

In Rio, Bolt and Phelps gave us the chance to be part of something we may never see again. More than a respite from the doping scandals, judging controversies, economic crises and political corruption looming in the background, they turned these Olympics into the party that organizers had promised it would be (well, that and the actual party at the electric beach volleyball venue in Copacabana).

Ledecky and Biles, meanwhile, are a reminder that such moments could come again–if we’re lucky. Before Biles took the floor for that final step on her way to the individual gold, she hugged her teammate Aly Raisman. Few gymnasts make it back to the Olympics; the sport is too demanding and the window for success too small. Yet Raisman and teammate Gabby Douglas both competed in their second Olympics in Rio. Raisman completed the routine of her life and won silver in the floor exercise, crying tears of joy as eight years of pent-up emotion poured out.

Biles said later that it took all she had to stop from crying then too. But she stuffed it inside–handling the pressure with the ease of Rio’s all-time greats.

Write to Sean Gregory at sean.gregory@time.com.

This appears in the August 29, 2016 issue of TIME.

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