(CNN) Health concerns prompt some to say they won't show up. A spate of violence spurs calls for stepped-up security. And some worry stadiums might not be finished before the opening ceremony.
Serious questions are looming over whether Rio de Janeiro really will be ready to host the Summer Olympics in less than a month.
If this sounds familiar, it should. Fears over problems ruining the Olympics have become as much a part of the run-up to the Games as scenes of athletes handing off the iconic torch as the competition nears.
Opinion: Should we panic about Rio Olympics? Get real
Here's a look at some of the concerns people were talking about before past Olympics around the world -- and what ended up happening once the Games got started:
The Belgian city was awarded the Games to honor the suffering the country had faced during World War I. But there was a flip side; organizers didn't have enough time to clean up wartime rubble.
The stadium wasn't finished. Athletes slept on cots in crowded rooms. And not many people attended the events, since few were able to afford tickets, according to Encyclopedia Brittanica.
But despite the hiccups, the competition went ahead as planned, with the Olympic flag flying overhead for the first time
Student movements in countries around the world were gaining steam as the 1968 Olympics neared. And the host of the Games, Mexico, was no exception.
On October 2, 1968, tensions between the government and tens of thousands of student protesters boiled over. Activists claim government forces cracking down on opposition in the leadup to the Games killed dozens -- possibly hundreds -- of people at a rally in Mexico City's Tlatelolco neighborhood.
It was less than two weeks before the Opening Ceremony. Organizers decided the Games would go on -- a move that sparked fears among international journalists who'd witnessed the violence.
During the Olympics themselves, there weren't major security problems. But a protest at the event drew international attention: the Black Power salute American sprinters Tommie Smith and John Carlos made after winning their medals.
There were plenty of fears that global politics could get in the way of the 1972 Olympics. Before the Games, a group of African nations had threatened to boycott until officials voted to ban Rhodesia from participating. Cold War tensions provided an uneasy backdrop for the competition, as West Germany prepared to present its new, democratic face to the world.
In an effort to show a demilitarized Germany, security around the Olympic Village was lax. Palestinian terrorists scaled a wall there on September 4, 1972, killing two Israeli athletes and taking nine others hostage. The hostages were later killed in a botched rescue mission.
Still, even after the Munich massacre, International Olympic Committee President Avery Brundage was resolute, proclaiming in a speech after the siege ended, "The Games must go on." Competition restarted after a 34-hour suspension.
The stadium built for the Montreal Games was called "The Big O." But it quickly earned a new nickname: "The Big Owe."
Its much-vaunted retractable roof never worked during the 1976 Games. The iconic leaning tower wasn't completed until more than a decade afterward. In all, the final bill was almost 12 times the original estimate -- and it took more than three decades to pay off the debt.
But Montreal's mayor, a former Canadian sports minister, says it was worth it, no matter the cost.
"It's not about concrete. It's about people," Denis Coderre told CNN in a recent interview. "I still have goosebumps. I remember the people when they were cheering, and then you forget about the infrastructure. You just felt that, 'Hey, this is something special.'"
The Montreal Expos baseball team, now the Washington Nationals, made Olympic Stadium its home for decades, and the facility had chronic problems.
Atlanta, too, faced construction concerns before it hosted the Summer Olympics in 1996. One person was killed when a steel lightning tower collapsed onto a grandstand as workers finished building a new stadium for the event.
And as fears about terrorism loomed months before the 1996 Games, officials boasted the centennial Olympics would have the most sophisticated security in the event's history, with state-of-the art surveillance keeping athletes and spectators safe.
An explosion shattered that sense of safety more than a week after the Games began. The Centennial Olympic Park bombing led to the deaths of two people, a bystander who died in the blast and a Turkish cameraman who died of a heart attack as he rushed to film the scene. The explosion injured more than 100 others. But the Games went on as scheduled that day.
It took authorities more than seven years to catch bomber Eric Rudolph, who later said he'd been aiming to knock out the city's power grid and shut down the Olympics to shame the United States for its legalization of abortion.
Reporters covering the runup to the 2004 Summer Olympics in Athens said the city was in a race against time. A series of bomb blasts in the Greek capital months before the Games began sparked security concerns. And for the first time, the International Olympic Committee took out an insurance policy to prepare in case the Games were canceled.
Once the competition began, organizers faced another hurdle: persuading spectators to buy tickets.
"In the Olympic tennis stadium, Venus Williams' grunts echoed loudly off several thousand empty seats," a CNN report at the time said. "There were so few people at the gymnastics preliminaries that it looked like a high school meet."
Now, more than a decade after construction delays dogged the Games, some of the stadiums built for the event are serving a different purpose: housing a flood of refugees streaming into Greece.
Beijing, too, faced construction woes in the leadup to its stint hosting the Games. And in a series of sweeping raids months before the competition started, authorities said they foiled a bomb plot by Islamist terrorists who aimed to target hotels, government buildings and military bases during the 2008 Summer Olympics.
But some athletes said pollution was their biggest worry. Health concerns prompted an asthmatic distance runner to pull out of the marathon. A U.S. triathlete said he was training wearing a mask. And a week before the competition started, China announced an emergency smog plan aimed at cutting down pollution by shuttering factories and stopping construction across the city.
Most fans, though, said the Games were a success. And it won't be long before China gets another chance to make an impression. Beijing is hosting the Olympics again in Winter 2022.
The 2010 Winter Olympics in Vancouver began with news of the death of Georgian luger Nodar Kumaritashvili -- a fatal training accident that called into question the track's safety.
Critics also complained about the warm, rainy weather at the Games. And officials quickly realized they were running low on a key ingredient: snow.
Efforts to make sure there was enough of the fluffy white stuff almost could have qualified as an Olympic event, the Guardian newspaper quipped at the time.
Helicopters airlifted snow. Trucks hauled in snow. Cannons shot ice and water out onto the slopes.
In the end, there was enough to go around, and Canada raked in a record number of gold medals.
The hashtag #SochiProblems gained steam on social media soon after the 2014 Winter Olympics started.
There were the packs of stray dogs that Russian authorities reportedly tried to exterminate. There was an international outcry after Russia passed a controversial law banning the public discussion of gay rights and relationships anywhere children might hear. There were security concerns, particularly after a suicide bomber killed 16 people at a train station in the Russian city of Volgograd less than six weeks before the competition started.
Once the Games got going, the gaffe that drew the most attention was an Olympic ring's failure to open during an Opening Ceremony performance.
But another kind of ring -- the so-called "ring of steel" around the city -- drew praise for preventing an attack in the region during the Games.