Their whereabouts may be a mystery. But these treasures by the likes of Leonardo, Caravaggio and Jan van Eyck could still turn up. If you’re a budding Indiana Jones, here are some clues to start you on your quest…

Imagine a museum of lost art. It would contain more objects than all of the world’s museums combined. Only a modest percentage of the works created through history survive intact today. For many pre-modern artists, not to mention those of the ancient world, many more works are known of (thanks to references to them in texts or other sources) than are extant.

Some of these vanished masterpieces are definitively gone, their destruction documented: most (but not all) of the seven wonders of the ancient world; Leonardo’s Horse statue (used as target practice by French archers after they took over Milan in 1499), or Rogier van der Weyden’s Justice Cycle (consumed by fire, along with the rest of the Golden Chamber in Brussels). But what really stirs the imagination are not the definitive tragedies of artefacts known to have been ruined, but the stories of artworks that are lost – stolen, mislaid, hidden and forgotten – and might be retrieved.

In art terms, lost could mean for ever, or simply that current whereabouts are unknown. Important works resurface with just enough regularity to inspire hope that lost art may eventually be found. A case in point is Leonardo’s Salvator Mundi, missing for centuries, covered in dirt, misattributed, thought all but worthless and now the world’s most expensive artwork.

The following gallery of lost works is meant for optimistic treasure hunters. It’s festooned with works that are lost but for which there is reasonable hope they remain intact and will be found again. Today we focus on what you should keep an eye out for, should you wish to unleash your inner Indiana Jones …

Painted over

Leonardo da Vinci’s The Battle of Anghiari

In terms of lost art, nothing has received quite the press of Leonardo’s unfinished fresco secco. It was made in 1505 on a wall in the grand meeting hall of Florence’s Palazzo Vecchio, an intentional artist’s duel with Michelangelo, who was commissioned to illustrate a different battle scene on the opposite wall. But The Battle of Anghiari was never finished, and it had been commissioned at a time when the ruling Medici family were ousted from Florence.

Facebook Twitter Pinterest Clues … art experts probe a wall at the Palazzo Vecchio in 2012, in search of Leonardo’s fresco. Photograph: Dave Yoder/AFP/Getty Images

When they returned, Duke Cosimo commissioned his architect, Giorgio Vasari, to renovate the room, increasing its size and to paint it with a new fresco cycle showing Medici military victories. But Vasari, the first art historian, was a great admirer of Leonardo and it is unlikely that he willingly painted over the Anghiari fresco. He planted a clue for us to follow: In that immense room, the Salone dei Cinquecento, there are only two words painted in: Cerca trova. Seek and you shall find.

Scholars believe Vasari built a false wall over Leonardo’s painting, to protect it while still fulfilling his commission – a trick he used to successfully preserve Masaccio’s Holy Trinity, one of the most important paintings in history, when he renovated the church of Santa Maria Novella around 1570. The fresco was only rediscovered in 1860. There is hope that Leonardo’s Battle could likewise see the light of day, but its excavation has been tangled for years in the famously convoluted Italian bureaucracy. The story of Battle of Anghiari is told in Jonathan Jones’s fine book, The Lost Battles, and in my last book, Collector of Lives: Giorgio Vasari and the Invention of Art.

Blade stunner

Masamune Honjō’s samurai sword

Japan’s most famous swordsmith, Goro Nyudoo Masamune, made this quasi-legendary katana – said to be perhaps the finest sword ever made – in the early 14th century. It was wielded in combat over the course of centuries, getting its name from a 17th-century owner, General Honjō Shigenaga. The story goes that another samurai attacked Honjō with this sword and split his helmet in two with a single blow, but Honjō won the fight and took the sword as his prize. It was worn by the Tokugawa shoguns and declared a national treasure of Japan in 1939. It disappeared, along with a collection of 15 prized swords, in January 1946, when these blades were taken by someone who appeared to be an American allied officer. None has been recovered.

All-time heist

The Gardner Loot

Facebook Twitter Pinterest $10m reward … Chez Tortoni, 1878-80, by Édouard Manet. Photograph: Bridgeman Art Library

In March 1990, 13 objects, worth an estimated $500m, were taken from Boston’s Isabella Stewart Gardner Museum, including paintings by Manet and Vermeer. It has been called the highest value peace-time property theft in history. The works are still missing, despite the reward for their recovery having been recently raised from $5m to $10m. Word is that those who know where the art is stashed have died, so it is a matter of luck if and when they will be stumbled upon.

By-the-book burglary

Jan van Eyck’s Righteous Judges panel from the Ghent Altarpiece

Facebook Twitter Pinterest Most taken … The Adoration of the Mystic Lamb, from Jan van Eyck’s Ghent Altarpiece. Photograph: Alamy

Van Eyck’s Ghent Altarpiece holds the dubious distinction of being the most-stolen artwork in history. The object of 13 crimes over six centuries, it has been burgled, all or in part, six times (dwarfing the runner-up, Rembrandt’s Portrait of Jacob de Gheyn at the Dulwich Picture Gallery, which was stolen a mere four times). All of the altarpiece’s 12 panels are now intact, but one is not the original. The panel depicting the Righteous Judges was stolen in 1934 and never found. The mastermind behind its theft from the cathedral of St Bavo in Ghent was a tubby stockbroker obsessed with the novels of Maurice Leblanc and his gentleman burglar, Arsène Lupin – he modelled the heist on the plot of a story called The Hollow Needle. This panel hung for many years behind the rood screen of a small church in rural Belgium, but its current whereabouts are unknown.

Fed to pigs?

Caravaggio’s Nativity with San Lorenzo and San Francesco

Facebook Twitter Pinterest Seismic loss … Caravaggio’s Nativity with St Francis and St Lawrence, 1609. Photograph: Heritage Images/Getty Images

No 1 on the FBI’s “most-wanted stolen works of art” list is a Caravaggio altarpiece swiped in 1969 from the church of San Lorenzo in Palermo. It was taken by members of Cosa Nostra, nearly found by British journalist Peter Watson, and a Mafia informer later claimed the painting had been damaged in an earthquake and fed to pigs. Let’s hope not.

Spoils of Ulay

Carl Spitzweg’s The Poor Poet

Facebook Twitter Pinterest Hitler’s favourite … The Poor Poet by Carl Spitzweg. Photograph: Leemage/Corbis

In 1976, performance artist Ulay stole from the New National Gallery in Berlin what was known as Hitler’s favourite painting, and brought it to the home of a poor, immigrant Turkish family, to hang it on the wall. He then phoned the gallery and turned himself in. This theft-as-performance-art resulted in the painting being returned to the gallery. So how is it still missing? It was stolen again in 1989 – that time for real – and has never been found.

Vanished volumes

Giorgio Vasari’s Libri dei Disegni

Facebook Twitter Pinterest Instruction manual … a page from Libro dei Desegni by Georgio Vasari. Photograph: Christie’s Images/Bridgeman Images

Of all the lost artworks that could fill our museum of lost art, the “books of drawings” collected by Vasari is perhaps the most apt. It was, in many ways, a portable proto-museum, before the term “museum” (museo) was in regular use. It was a collection of 12 large folio blank books, into which Vasari pasted drawings he had collected by the most famous artists of the 14th to 16th centuries, from Giotto to Michelangelo. Vasari added his own illustrations and motifs based on the style of the artist featured. Today, only a handful of individual pages from the Libri are extant, but what a treasure the whole collection would be, were it found.

Revealed by Isis?

The Hanging Gardens of Babylon

Facebook Twitter Pinterest The city walls of Babylon in an engraving by Friedrich Johann Bertuch. Photograph: Florilegius/SSPL via Getty Images

Of the seven wonders of the ancient world, only the Great Pyramid of Giza is known to have survived, but the Hanging Gardens may have, as well. Archaeologists have recently considered that the elaborate terraced gardens of the Assyrian kings may not have been in Babylon at all, but at Nineveh. In fact, when Islamic State blew up parts of Mosul, they may have inadvertently revealed previously buried and unknown structures from ancient Nineveh that some scholars believe were part of a terraced garden better matching the descriptions of the Hanging Gardens than anything known in Babylon.

Heads you lose

Animal heads from the Zodiac Water Clock

Facebook Twitter Pinterest A bronze pig’s head from the clock fountain. Photograph: MCT via Getty Images

The 2009 auction of the estate of Yves Saint Laurent made headlines when included in the sale were two of the 12 bronze animal heads that had once decorated a great fountain in the Old Summer Palace in Beijing. The palace complex had been looted by British and French soldiers in 1860, during the opium wars, and the rat and rabbit heads had been considered lost ever since. They were eventually acquired by China, and now seven of the heads are displayed at Chinese museums. A snake, sheep, rooster, dog and dragon remain lost. At least for now.

Pilfered porn

Marcantonio Raimondi’s The 16 Pleasures

Facebook Twitter Pinterest Erotica … The 16 Pleasures. Photograph: akg-images

Considered the first work of printed pornography, this collection of erotic engravings by Renaissance master Marcantonio Raimondi (based on a lost painting cycle by Giulio Romano) are all likely lost, despite the fact that they were considered great works of art. Pope Clement VII was unimpressed and sought to acquire and burn all copies of the first edition and the second (in which the engravings were accompanied by sonnets penned by a famous wit, Pietro Aretino). But hope springs that some of the prints survived, and pirated versions certainly do, including one published by two 17th-century century fellows at All Souls College, Oxford, who shepherded the first English edition, entitled Aretino’s Postures, as an early publication of Oxford University Press (before the fuddy-duddy dean confiscated the copper plates and shut down the operation).

• Noah Charney’s The Museum of Lost Art is published by Phaidon.