If people remember anything about the Iraq Museum, it is most likely the televised images of it being looted in 2003 as American troops watched from their tanks.

Statues too heavy to move were knocked from their pedestals, their 3,000- and 4,000-year-old shoulders bashed to powder. Some lost their eyes or one side of their face. Glass cases were shattered, their contents gone or thrown on the floor.

One of the museum’s most treasured art works was the Warka vase, with carvings dating back five millenniums showing that even then the ancient Mesopotamians grew wheat and fruits, wove cloth, and made pottery. When someone walked off with it, a bit of human history was lost.

The same was true of the Golden Lyre of Ur, a 4,500-year-old musical instrument inlaid with gold, silver and carnelian.

I was there in 2003 on the second morning of looting and was stopped about 150 feet from the museum entrance by crowds of Iraqis rushing by clutching clay objects I could not identify. They also carried more prosaic items — file cabinets, chairs and spools of electrical wire.

This spring, 16 years later, I was back at the museum. It had reopened in 2015 after conservators had repaired some of the damage and European countries, among others, had helped restore several galleries. Still, I expected to see bare rooms and empty niches.

Instead, I found that despite the loss of 15,000 works of art, the museum was filled with an extraordinary collection.

In a well-lit gallery, I stared up at two majestic alabaster creatures at least 12 feet tall but looking even taller because they were set on plinths.

They had the bearded faces of men, four or five legs, the wide wings of eagles, and the bodies and tails of bulls. Known as lamassu in the ancient Sumerian language, they were thought to be spirit guardians so they were set at city gates, palace entrances and the threshold of throne rooms.

Here, they watched over two long rooms of friezes that showed ancient Mesopotamians carrying tribute or walking beside their horses, which were finely carved with muscled flanks and elaborate reins.

The lamassus and friezes survived the looters because they were too heavy to haul away.

Art historians and archaeologists know how exceptional the collection is. But despite Baghdad’s relative safety today, neither the city nor the museum have yet to become a major destination for Iraqis, much less foreign tourists.

“There are things there that are nowhere else in the world, especially from early Mesopotamian history,” said Christopher Woods, the director of the University of Chicago’s Oriental Institute, who recently visited Baghdad.

“It’s a textbook collection,” he said.