They were, quite literally, robbing the cradle. Mesopotamia is called the "cradle of civilization" and with good reason. It is here that there is the first evidence of villages and cities; the wheel and the plough were invented here, as were writing, epic poetry, and God.
Mesopotamia is also the cradle of archaeology. Europeans began digging here in the mid 19th century. Many of the things they dug up went to museums. Others did not.
There's always been a lively underground trade in Mesopotamian artifacts. And with the looting of the museum, it's bound to become a lot livelier, correspondent Bob Simon reports.
"Much of the material that passes through the market is illegal," says archaeologist John Malcolm Russell, who specializes in Mesopotamia. "It's illegally excavated in the country of origin, leaves illegally, and passes underground."
"It's clear, though, that the market must be enormous. And that someone is going to great, to a lot of trouble, to feed that market with a huge volume of works."
Russell learned about that market when he was digging at the ancient city of Nineveh. That's the place in northern Iraq where, according to the Bible, Jonah wound up after being spit out by that whale.
The best of what the archaeologists unearthed ended up in Baghdad's National Museum, which housed the world's largest collection of Mesopotamian antiquities.
Taking a stroll through the museum was a trip back in time - an almost magical stroll through the millennia. Artifacts were displayed, not only for their beauty, but to show civilization where it came from.
Director Donny George spent years building the museum's collection.
"You could trace the development of agriculture, the development of writing," says George. "We had the development of social traditions, development of art, and you could see the first wheel. You could see the first signs for writing. They were all here."
But not any more. On April 11, while conquering American troops were guarding Iraq's oil ministry, they were not protecting Iraq's museum. Armed thieves walked right in.
Defense Secretary Donald Rumsfeld seemed to suggest it wasn't all that serious.
"The images you are seeing on television you are seeing over, and over, and over," said Rumsfeld. "It's the same picture of some person walking out of some building with a vase, and you see it 20 times, and you think, 'My goodness, were there that many vases?' Is it possible that there were that many vases in the whole country?"
In fact, it wasn't just vases. It was everything. Everything of value, that is. The looters knew what they were doing.
"They knew what they wanted. Because we found in the museum some glass-cutters," says George. "These are glass-cutters, so they were equipped with these things to go inside and cut the showcases."
They passed up the reproductions and went right for the real stuff. Genuine, unique, priceless. And irreplaceable.
Lost from the Sumerian gallery was the so-called sacred vase from Warka, which goes back to Sumerian times, about 3200 years B.C.
Thousands of lesser-known but valuable items were also taken. And, George fears, they will resurface very soon and very far from the cradle of civilization.
"They might pop up in Switzerland, in England perhaps," says George. "They might pop up also in the United States, in Israel, or in Japan. And what we are afraid of is that they might go to private collections. Then, it's a tragedy, because we might not find them."
Just yesterday, George asked the United Nations to declare a temporary moratorium on the trade of all Iraqi antiquities. But archaeologists say this is a classic case of locking the barn door after the horses have been stolen. The sale of plundered antiquities has always been illegal, but it has also been a bustling trade.
This is a lesson Professor Russell learned first-hand: "Where plunderers go in, thieves go in and either illegally dig up or break apart archaeological monuments for the market."
When Russell was in Nineveh in the 1980s, he helped excavate a king's palace. Inside, archaeologists found huge, intricately carved reliefs, carvings very similar to those in the Brooklyn Museum of Art.
"What I found at Nineveh was a slab this size, which I would have photographed in the palace. And then, a few years later, a museum, or collector, would offer me a piece, say, maybe a foot square. Only a small part of the figure," says Russell.
"It's possible to easily identify it as from that piece. The question then is what happened to the rest of the piece? How could you extract something from the middle of the slab without destroying the rest? And I was able to get a friend in Iraq to take pictures, and what he showed me was just small piles of rubble."
Looting, of course, is as old as war itself. But Russell says the market in stolen Iraqi antiquities really took off when sanctions sunk in after the first Gulf war. The only Iraqi commodities that Westerners wanted were oil and antiques.
The Iraqi government had the oil. Iraqi people had the shovels.
"What may have started out as sort of opportunistic night-time digging to feed your family turned into whole sites being ransacked by hundreds of people with shovels," says Russell.
"Organized, with clear, clear channels through middlemen out to the Western market. That made it possible for this, what some collectors call a 'golden age' of cheap, new, fresh Iraqi antiquities."
"I think archaeologists basically have been perpetuating this huge lie, literally," says Torkom Demirjian, who owns an antiquities gallery on New York's Madison Avenue – a place where old money looks for old objects.
Like many traders, he insists there's no network of looters and smugglers, no flood of stolen antiquities.
"There's a lot of stuff out there that are already in public museum collections," says Demirjian. "And there is not much else that is out there; there is not so-called 'fresh,' available material, as archaeologists would like to call it."
Demirjian says the law governing the sale of antiquities is the same law which governs all trade, the law of the market.
"You cannot create something because there is a demand for it. Usually, it is the supply that determines what demand there is," says Demirjian. "You cannot crank up your production lines and say, you know, 'Produce another Sumerian idol, produce another Greek pot.' It's just not possible."
So where do they get this stuff?
"There are those who own antiquities, who will come to us saying, 'We have this and this for sale, would you be interested?' That's the way," says Demirjian.
No matter who sells an artifact, there is one important question any buyer wants to know. Where did it come from?
The sales history of an item is called its provenance. And when an item comes from ancient Greece, auction house catalogs usually list long, detailed provenances. But the pedigrees for Iraqi antiquities are often vague or non-existent.
But you don't need to go to an expensive gallery to find an Iraqi artifact. Russell showed us how you can let your fingers do the walking through the Internet, right to sites like eBay. Of the hundreds of items listed, he zeroed in on one – a clay tablet.
The description? "Believed to be the world's oldest surviving written receipt for delivery of beer by a brewer."
"If you're going to ask me about the cradle of civilization, this is where beer came from," says Russell. "I mean, really. We're talking about fundamentals."
"It's upside down. It's been over-cleaned. Which to me is a hint of looting, although certainly not conclusive. There's no ownership history given."
Russell points out another part of the tablet's description: "This remarkable 4,000-year-old document is not of those recently plundered from Iraq. It has been held in the private collection of this present owner since prior to 1990."
"So, whatever it is, it's not looted, this person is insisting," adds Russell.
The Internet is the very low end of the antiquities business. People can get many of these things for less than a hundred bucks.
But Dermijian deals on the other end of the market - several digits more than anything on eBay. And when you buy his stuff, you also get a guarantee that it is kosher.
"We are on a prominent corner of Madison Avenue, and we don't have a sort of secret stash of objects that we don't, we will not show you," says Dermijian. "If you are a collector in this field, we will try our very best to find the material that's suited, that's absolutely part of our inventory and that's a public record."
He also says that the law places a burden on private dealers. "The burden is that we have to use due diligence," he adds. "You have to use your common sense, and if everything proves to be OK, then it's a very proper, legitimate purchase."
So what does Dermijian think of archaeologists who view private dealers like him as laundering looted material?
"Archaeologists are liars. I tell you this straightforward. They will say anything, do anything, to promote their incredibly radical ideology," says Dermijian.
The "radical ideology" that Demirjian is referring to is the law today in most Middle Eastern and Mediterranean countries - the export of antiquities is forbidden.
"What are we supposed to do," asks Demirjian. "Bus every child to Egypt so they can see Egyptian art in Egypt?"
Does Russell believe that the artifacts, the antiquities of a nation, should stay in that nation?
"I believe that, if that's the will of the people in the nation, that you have to respect that," says Russell.
But the deeper question is not whether an object stays in Baghdad or is moved to Brooklyn. As long as it is somewhere we can see it. Because it is ours, and when it is broken or looted or hidden away in some Swiss chalet, we suffer a loss that is quite simply immeasurable.