A lost painting is like a needle in a haystack. It may be out there, but finding it is a challenge.

In cases where you’re lucky enough to have a good idea where the thing might be, the challenge is simply a matter of persistence: just keep looking in that area until you find it. A missing painting by Johannes Vermeer would probably be in an attic somewhere near Delft, where he lived and worked, so finding that needle would be a simple matter of searching all the attics in the area. That’s how two of Vermeer’s paintings were found in the 20th century.

But what if your lost Vermeer is not so easy to locate? What if you don’t even know which continent it might be on? If that’s your situation then finding your needle becomes much more difficult.

It happened to Bill Brandt when he began to search for one of his most enigmatic photographs, “The Pond,” which had been taken for Vogue magazine in 1952. The picture was an unusual one for Brandt, who was known for his stark black-and-white landscapes, gritty urban street scenes and portraits of Londoners during the Blitz. But this time he had been asked to make a photograph of swans on

The problem is that, compared to the number of paintings that were painted in the past, there are relatively few left. “Art is ephemeral,” says Thomas Sokolowski, the director of the Art Institute of Chicago. “It’s created by human beings, and human beings are mortal. Things deteriorate.”

The rate of deterioration depends on the medium. Oil paint deteriorates slowly, but if a canvas is left out in the sun or exposed to moisture or mold, it can lose its luster in a generation or two. Watercolors fade. Prints turn yellow. Given enough time, even marble statues crumble.

Even when a work survives, art historians often have trouble finding it. Many works were destroyed during wars and revolutions. Others were destroyed by accident: Van Gogh once sent his famous painting “The Night Café” to his brother as a birthday gift (it was returned as undeliverable), and Picasso once cut up one of his own paintings and used it to wrap a present (he later regretted it). Even when they don’t get physically destroyed, many paintings are hidden away by families who inherit them with no idea of their value.

But sometimes a lost painting resurfaces. Here’s how to find one.

The point of the experiment was to find out how much value people would assign to a lost painting. How much would they be willing to pay for it, or to contribute toward its recovery?

The answer, as it turned out, was nothing. The painting had been lost for decades, but it wasn’t until it was offered for sale that anyone who saw it thought it might have value. If a painting by a great artist simply disappears from public view, then even if the artist is well known, no one will know whether the work is good or bad. And if you don’t know whether the work is good or bad, then you won’t know how much money you can make from selling it.

And this explains something else: the surprising number of famous paintings that have disappeared and never been found. In some cases all we have are rumors—rumors that are interesting in their own right because they show how people think about art.

For example, there’s a story about two famous paintings by Vermeer, “The Concert” and “The Art of Painting,” which were said to hang on either side of Rembrandt’s “Night Watch” in the Amsterdam Town Hall in 1715. During the French occupation of Holland in 1747, these paintings

There are tens of thousands of lost works of art, and the number grows every year. Paintings are stolen from galleries, watercolors are destroyed in fires, canvases are lost in floods, and many more pictures are misplaced by their owners—who may or may not report their losses.

The facts about art theft may sound startling. But statistics only hint at the profound human effects of art theft and the financial toll it exacts on auction houses, museums, galleries and private collectors.

The Art Loss Register was founded in 1991 by Julian Radcliffe to help combat the growing problem of art theft and fraud. The ALR is now a worldwide network, with a searchable database containing information on over 130,000 missing works of art.*

A tiny painting, about the size of a postcard, by the Italian artist Amedeo Modigliani was discovered in 2005. Its whereabouts had been unknown since 1917. The little canvas—a portrait of a woman’s head with a Mediterranean landscape background—had been rolled up, covered with dust and stuffed beneath a bed in Paris.

The painting was one of hundreds that Modigliani had created over a period of three years, from 1916 to 1919. At the height of his fame—he was often called the “Italian Matisse” for his cubist-influenced style—Modigliani produced about 300 paintings, drawings and sculptures each year. He died at 35 on January 24, 1920, after spending his final years in poverty and relative obscurity.

About 100 works by Modigliani remain in museums or private collections today. The rest are lost; they were either destroyed or are still sitting somewhere gathering dust.

A few years ago, one of the most celebrated works of 17th-century Dutch painting was discovered in a museum basement. “The Young Archer” was painted by Frans Hals, the most famous portraitist of his time; it was also one of his first known works. It depicts a young man dressed in black, holding a bow and aiming at an archery target. One scholar called it “the Mona Lisa of the 17th century.”

Toward the end of the 20th century, however, the painting fell out of favor with scholars and was consigned to storage. It had been badly damaged at some point—possibly by overcleaning or exposure to light—and many attributed its loss of fame to this damage. But when it was brought out again for an exhibition in 2011, experts were stunned to find that it wasn’t as damaged as they had thought; in fact, it was in relatively good shape. And not only that: They realized that the painting’s condition had been misrepresented all along. In fact, “The Young Archer” hadn’t been destroyed by cleaning or light; someone had cut off the top third of it. This information led scholars to take a second look at Hals’s early work and prompted a new appreciation of

In the early 1980s, a French scholar named Pierre Schneider was browsing through the collections of the Metropolitan Museum of Art when he came upon an old master: a portrait of a young woman with a pensive expression on her face, her skin smooth and pale.

Taken aback, he pulled the painting from its frame to make sure it wasn’t simply a copy. He checked for labels and stickers and examined the canvas. The more he studied it, the more convinced he became that this was an unknown masterpiece.

What made his find all the more remarkable was where he had spotted it: in the museum’s collection of 19th-century art. Old master paintings were not what scholars expected to find in such a setting.

The painting turned out to be a portrait of a Milanese noblewoman by Girolamo da Carpi, one of Italy’s most influential painters in the decades after Michelangelo’s death in 1564. Judging from documents in the Met’s archives, Mr. Schneider deduced that it had been acquired by one of its founding trustees, J. P. Morgan, who never even bothered to exhibit it.

With this discovery, Mr. Schneider believed that he had solved one of modern art history’s great mysteries: Who painted “Port