The patterns of the heists were evident only later, but their audacity was clear from the start. The spree began in Stockholm in 2010, with cars burning in the streets on a foggy summer evening. The fires had been lit as a distraction, a ploy to lure the attention of the police. As the vehicles blazed, a band of thieves raced toward the Swedish royal residence and smashed their way into the Chinese Pavilion on the grounds of Drottningholm Palace. There they grabbed what they wanted from the permanent state collection of art and antiquities. Police told the press the thieves had fled by moped to a nearby lake, ditched their bikes into the water, and escaped by speedboat. The heist took less than six minutes.

A month later, in Bergen, Norway, intruders descended from a glass ceiling and plucked 56 objects from the China Collection at the KODE Museum. Next, robbers in England hit the Oriental Museum at Durham University, followed by a museum at Cambridge University. Then, in 2013, the KODE was visited once more; crooks snatched 22 additional relics that had been missed during the first break-in.

Had they known exactly what was happening, perhaps the security officials at the Château de Fontainebleau, the sprawling former royal estate just outside Paris, could have predicted that they might be next.

With more than 1,500 rooms, the palace is a maze of opulence. But when bandits arrived before dawn on March 1, 2015, their target was unmistakable: the palace's grand Chinese Museum. Created by the last empress of France, the wife of Napoleon III, the gallery was stocked with works so rare that their value was considered incalculable.

In recent years, however, the provenance of those treasures had become an increasingly sensitive subject: The bulk of the museum's collection had been pilfered from China by French soldiers in 1860 during the sack of Beijing's Old Summer Palace.

In the low light before daybreak, the robbers raced to the southwest wing and shattered a window. They climbed inside, stepping over broken glass, and swiftly went to work dismantling the empress's trove. Within seven minutes, they were gone, along with 22 of the museum's most valuable items: porcelain vases; a mandala made of coral, gold, and turquoise; a Chimera in cloisonné enamel; and more.

The police arrived quickly, but there was little to be done. Before vanishing, the criminals had emptied a fire extinguisher, spraying its snowy foam perhaps in the hopes that it would erase their fingerprints, hide their footprints, and remove any lingering clue as to who they were. “The thieves knew what they were doing and exactly what they wanted,” the museum's president, Jean-François Hebert, told the press. They were “probably very professional.” The theft, he added, was a “terrible shock.” But maybe it shouldn't have been.

In the years since the Fontainebleau heist, the robberies have continued throughout Europe—sometimes in daring, cinematic fashion. The full scale of the criminality is impossible to pinpoint, because many heists never make the headlines. Security officials and museum boards are sometimes reluctant to publicize their own failures, both to avoid embarrassment and to save on the cost of security upgrades.

But the thefts that were made public bear striking similarities. The criminals are careful and professional. They often seem to be working from a shopping list—and appear content to leave behind high-value objects that aren't on it.

In each case, the robbers focused their efforts on art and antiquities from China, especially items that had been looted by foreign armies. Many of these objects are well documented and publicly known, making them very hard to sell and difficult to display. In most cases the pieces have not been recovered; they seem to simply vanish.