Here are five things to know about the minnows based in a pro-Russian breakaway region of Europe's poorest country, Moldova:
The young club founded in 1997 is based in Transnistria, a tiny breakaway would-be state one-fifth the size of Wales.
The region, which broke away from Moldova in the wake of a brief civil war after the collapse of the Soviet Union, has its own currency, border police, army and cellular network.
Propped up by free Russian gas and some 1,500 troops, a 2006 referendum showed 97 percent of Transnistrians want the state to join Russia.
But the breakaway region has not been recognised by Russia, let alone the international community.
That allows Sheriff to play in the Moldovan league, through which they can qualify for European competitions.
Small budget, foreign players
With a squad made up mostly of foreign players, Sheriff have dominated their domestic league, winning six straight titles and 19 out of the last 21.
Their starting line-up against Real Madrid featured two Brazilians, two Greeks, two Colombians, one Peruvian, one Uzbek, one Ghanaian, one Luxembourger and one Malian.
But their budget is miniscule when it comes to Europe's biggest footballing stage, with the entire squad valued at just 12 million euros ($14 million), according to website Transfermarkt.
For comparison, Real Madrid midfielder Casemiro alone is valued at nearly six times as much.
The club have played four times in Europe's second-tier competition, the Europa League, but this year was the first time they qualified for the Champions League group stage.
Sheriff are owned by an eponymous company founded in the early 1990s by two former Soviet police officers that has an economic and political monopoly on Transnistria.
The region has long been described as a smuggler's paradise and Sheriff's ownership has been accused of corruption.
Among the conglomerate's many businesses are supermarket and gas station chains that feature the company and football club's five-pointed sheriff's star as a logo.
In 2015, investigative outlet RISE Moldova dubbed Transnistria "Sheriff Republic" after finding that one third of all the money from the separatist enclave's budget was paid out to companies owned by Sheriff.
Cognac, caviar, casino
Sheriff owns the KVINT cognac distillery that was founded in 1897 during the Russian Empire.
It also has a subsidiary named Aquatir that runs a sprawling caviar farm that produces prised beluga roe.
Each year Aquatir harvests seven tonnes of black caviar, sold for $22 to $90 per 50 grams (1.75 ounces).
The company also has some 20 albino belugas that next year will be mature enough to produce a gold-tinted white caviar sold for $20,000 (17,000 euros) per kilogram.
If cognac and caviar are not enough to lure tourists to Tiraspol, Transnistria's administrative hub and home to FC Sheriff, visitors can also visit the Sheriff casino downtown.
Despite its capitalist successes, Transnistria remains a living museum of Soviet iconography.
A statue of Lenin towers over the centre of Tiraspol, while his bust stands in front its City Hall still named the House of the Soviets.
To top it off, Transnistria's flag and coat of arms feature a hammer and sickle.
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