If the thieves who robbed Rotterdam’s Kunsthal exhibition this week don’t have a plan, the stolen art could quickly become a burden. Paintings, sculptures and other cultural treasures can be hard to match with a buyer willing to overlook questionable provenance. Just ask the trafficker who lucklessly tried for 20 years to sell a statue head of Nero’s mother stolen from Pompeii before its recovery was announced on Thursday.

But, experts say for criminals with connections, it’s a low-risk, high-reward job, especially for lesser known pieces.

Art theft is the third most lucrative crime in the world, after drugs and illicit arms sales, according to Interpol and the FBI. Films glamorize it, and the punishment for those who are caught is too light to be much of a deterrent.

Stolen art disappears into the underworld quickly. Much of it is never found. Paintings have been buried, stashed in storage units, given as gifts to the unwitting, traded for drugs, held for ransom, hung on the walls of criminals, and sold on eBay.

Straight cash transactions appear to be rare — at least for high-profile thefts like the one in Rotterdam. Anyone legitimate enough to demand where a painting came from is going to come across it in news stories and databases of stolen artwork.

“We either see artwork being recovered very quickly after the theft or decades later, very little in-between,” said Chris Marinello, executive director of the Art Loss Register, whose job it is to track stolen art after the police trail has run cold.

But it’s been 22 years since the theft of $300 million in works from the Isabella Stewart Gardner Museum in Boston — the largest single property theft ever. The case is unsolved and none of the 12 paintings has been recovered.

“It’s easy to steal artwork, and that’s why you see it happen, but it’s not easy to sell it. You steal a car, you steal a watch, there’s a market for that. You steal a Rembrandt, you steal a Picasso . It’s too recognizable,” said Geoffrey Kelly, the FBI agent leading the Gardner investigation.

That means many stolen works end up getting dumped. Five works stolen from the Paris Museum of Modern Art in 2010 may be gone forever. According to one French report, the thieves couldn’t quickly resell the works and their fence panicked after a series of arrests, destroying the canvases and throwing away the remains — a Picasso, a Braque, a Modigliani, a Matisse and a Leger.

In another case, Marinello said, a British woman whose boarder gave her a painting years before contacted him to determine its worth, only to learn it was stolen. She was innocent, an unwitting victim of someone who couldn’t unload his loot.

And in Ireland, IRA thieves plundered the art collection of Sir Alfred Beit in the 1970s, demanding ransom and freedom for political prisoners. Their demands weren’t met and the works were found in the trunk of a car. Beit’s collection was stolen again in 1986. This time, the thief buried 11 paintings while trying to sell them. He eventually traded two for drugs and stashed one behind a couch before the collection was recovered.

Then there is “The Scream,” one of two Edvard Munch masterpieces stolen from an Oslo museum in 2004 and recovered in 2006. Police have never offered details on the painting’s whereabouts for those two years, but by the time they were found, they had sustained water damage and tears. Not a sign of a theft commissioned by a connoisseur.

Despite the complications of fencing stolen art, it clearly can be done, especially by thieves with connections. Estimates range from $6 billion to $9 billion in global sales — a sign of both how lucrative the market is and how little known.

It’s anyone’s guess what happened to the Gardner paintings, for example — or whether anyone still alive even knows. The $5 million reward hasn’t brought them to light, nor have promises of immunity.

“It’s easy to move around, easy to enter the black market,” said Anthony Roman, a New York-based security expert. And, he said, even though the returns on the black market are a fraction of what the art could fetch on the open market, “There is still a fortune to be made. The risk of getting caught is very, very low.”

Prosecutions generally fall under burglary, extortion or — at most — robbery statutes. Sentences are relatively short.

“Art theft is not murder, but still the penalties could be enhanced a bit to discourage people,” said Marinello.

In one infamous case, a compulsive French art thief named Stephane Breitwieser told a court he stole more than 200 works from small museums across Europe, keeping most of them at his home purely for his own enjoyment.

He was sentenced to 26 months in prison in 2005 — and then was arrested again in 2011 after investigators said they found 29 works of art at his apartment.

Insurance companies absorb most of the losses. In the Rotterdam case, the payout is likely to climb to the tens of millions of dollars — but that causes costs to rise in the future for everyone in the art world, said Coco Soodek, a Chicago lawyer who specializes in the field. And it makes private collectors more reluctant to put their works to go on public display in the future.

“The more the art world becomes the target for theft,” she said, “the more expensive it is to insure the product.”

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