The International Olympic Committee has barred the Russian team from competing in Pyeongchang in February over widespread doping at the last edition of the Winter Games in 2014.
However, they will be allowed to compete as "Olympic Athletes from Russia" under the Olympic flag. Gold medalists won't hear the Russian anthem played on the podium.
The IOC says the OAR team will be invitation-only, picked by a panel of anti-doping and medical officials from various organizations.
To be invited, Russian athletes must meet the usual Olympic qualifying standards but also "be considered clean to the satisfaction of the panel," meaning they can't have been previously banned for doping and must face extensive pre-Games drug testing.
It's not yet clear if Russian athletes plan to challenge these requirements in court. An IOC attempt to bar Russians with previous doping bans from last year's Summer Olympics was overturned at the Court of Arbitration for Sport.
Under the current IOC rules, here's a look at how "Olympic Athletes from Russia" might fare in Pyeongchang:
Russians have won men's hockey gold under the Olympic flag before.
Back in 1992, shortly after the collapse of the Soviet Union, players from ex-Soviet countries teamed up, including future Stanley Cup winners Alexei Kovalev and Sergei Zubov. It wasn't a punishment but political expediency in a chaotic political situation.
This time around, Russia's neutrals would have a good shot at gold, in the absence of NHL players. Former NHL star Ilya Kovalchuk, now playing in Russia's Kontinental Hockey League, is keen to play. "We definitely have to go," he told Russian media after the IOC decision.
One obstacle could be KHL leadership, which previously threatened it might pull its players if Russia was punished over doping.
Russia's women's hockey team might be a contender for bronze but struggles to compete against the top two squads, the US and Canada. Some women's players have also been accused of doping offenses related to tampering with their 2014 Olympic samples, so eligibility is an issue.
Russia sent just one athlete to appeal to the IOC board on Tuesday, 18-year-old skating prodigy Evgenia Medvedeva.
It's easy to see why. Unbeaten in two years, Ms. Medvedeva is the clear favorite for women's skating gold, and in a sport where careers are short, "I don't know if I'll have another Games in my life after Pyeongchang," she told the board.
She's also not connected to any doping offenses from 2014, when she was just 14.
If Medvedeva goes to February's Olympics, she'd be joined by potential Russian medalists like pairs skaters Evgenia Tarasova and Vladimir Morozov.
Russia has never been an Alpine skiing power, but might have an outside shot at a medal under the Olympic flag.
Slalom specialist Alexander Khoroshilov in 2015 became the only Russian skier to win a World Cup event since 1981, when Russians still competed as part of the Soviet Union.
Three podiums last season show he could threaten the top three in Pyeongchang under the right conditions. Mr. Khoroshilov is based in Switzerland.
Key Russian skiers from the 2014 Olympics have already been banned by the IOC for doping, with four of Russia's five medals stripped.
Of the three Russian skiers who swept the podium in the 50-kilometer race on the final day in Sochi, the only one left is bronze medalist Ilya Chernousov, who now faces a possible upgrade to gold subject to IOC confirmation.
Still, a new generation of athletes could challenge for gold in Pyeongchang, led by Sergei Ustyugov, who won five medals at this year's world championships. IOC bans on skiers from Sochi will weaken Russia's strength in depth for relay events, which make up one-third of the program.
Under the IOC criteria, Russia should be able to field nearly a full team in biathlon, the country's most-watched winter sport.
Russia has been stripped of two medals from the Sochi Olympics, with three of the women's relay team banned, but the athletes concerned had already retired.
Seven-time world championship medalist Anton Shipulin could be the key medal contender for Russia, though he's started the new season slowly.
IOC rules could block Alexander Loginov, who returned from a two-year doping ban last season to win a world championship relay bronze.
Individual doping bans from the IOC have already devastated Russian medal hopes in the bobsleigh and stripped the country of two gold medals won in Sochi.
Russia's sleds were already depleted by retirements since Sochi, even before the top Russian pilot in the two-man and four-man events, Alexander Kasyanov, was handed an IOC lifetime Olympic ban earlier this month.
In a detail unlikely to impress the IOC, a former athlete banned in the Sochi doping investigation, Alexander Zubkov, is now in charge of the Russian Bobsled Federation and will oversee athletes' preparation.
Russia had been counting on Sochi gold medalist Alexander Tretyakov and bronze medalist Elena Nikitina to repeat their success in Pyeongchang, but both were banned by the IOC earlier this month.
The top Russian with hopes of competing as a neutral is Nikita Tregubov, who won a silver medal in a World Cup race Nov. 25 and dedicated it to his banned teammates.
On the women's side, medal hopes appear remote.
The IOC's rules on previous doping bans could rule out Russian skating star Denis Yuskov for a sanction he received after testing positive for marijuana in 2008, even though it's not a performance-enhancing substance.
Tuesday's ruling opens the way for six-time Olympic short-track champion Viktor Ahn to return to South Korea and contend for more medals.
Previously known as Ahn Hyun-soo, he switched allegiance to Russia after failing to make the South Korean team for the 2010 Winter Olympics, and his return in Pyeongchang will be hotly anticipated, regardless of which flag he competes under.
Women's skater Olga Fatkulina is ruled out after the IOC stripped her of her silver medal in the 500 meters from the Sochi Olympics earlier this month and banned her for life from the Games.
Two of Russia's gold medalists from the Sochi Olympics, the slalom snowboarders and married couple Vic Wild and Alyona Zavarzina, could make a return as neutrals, though they've yet to comment on the IOC decision.
Medals are potentially possible in other disciplines such as big air or snowboard cross.
There could be outside medal chances for "Olympic Athletes from Russia" in freestyle skiing, luge, and women's curling.
Whether or not they compete under their own flag, ski jumping and Nordic combined seem unlikely to result in any medals for Russians.
This story was reported by The Associated Press.