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As World War II raged, Adolf Hitler retained an ambition to build the world's finest museum in his hometown of Linz, Austria. He planned to call it the Führermuseum and hoped to stock it with the greatest works of art from around the globe — which he would obtain by looting collections and museums in occupied territories and hiding them until the war ended.

From 1942 until 1951, 365 men and women serving in the Monuments, Fine Arts & Archives division (MFAA) of the Allied forces dedicated themselves to stopping Hitler's dream from becoming a reality. Known simply as the Monuments Men, they recovered Nazi records from bombed-out cathedrals and followed leads across the continent in a bid to recover Europe's most splendid treasures.

In his new book Monuments Men: Allied Heroes, Nazi Thieves and the Greatest Treasure Hunt in History, American writer and art detective Robert Edsel tells the stories of seven of them, including America's top art conservator, a sculptor and an openly gay infantry private. Edsel spoke with TIME about the challenges they faced.

Why did Hitler want to build the Führermuseum?
He was a frustrated, aspiring artist. He had applied to the Academy of Fine Arts in Vienna as a painter and been rejected. He had been encouraged to reapply for architecture school and was rejected again. He believed that the majority of the jurors at the academy were Jews. He was determined to get back at them and diminish Vienna's cultural influence over Europe by rebuilding Linz. It was an industrial city and wasn't particularly attractive. He wanted to make it magnificent.

Did the Nazis target specific works, or was it more about grabbing whatever they could?
There were definitely works of art they were determined to steal. An example would be the so-called big three from Krakow — Leonardo's Lady with an Ermine, Rembrandt's Landscape with the Good Samaritan and Raphael's Portrait of a Young Man. The Nazis seized them within two months of the 1939 invasion [of Poland]. They didn't go where the works of art were supposed to be hanging in the museums. They went to the country house where they had been hidden because their intelligence was so good.

In the book you describe how the Monuments Men used recovered records, overheard conversations and diaries to track down various works. What was their main tactic?
They would go around and interrogate people. They would look for museum directors and curators and ask where pieces of art were. They'd hear vague things like, "Well, the last time we saw it the armies were going east," or "The Nazis came and said 'We're taking these works to safeguard them' " — a very utilitarian word to describe theft and robbery. Eventually they started finding people who knew things, and those people would send them to see someone else who knew something more specific.

Where are some of the places they uncovered artworks?
Some were in castles like Neuschwanstein in Bavaria. The Veit Stoss altarpiece [a 15th century three-story wooden altarpiece and Polish national treasure] was in a tunnel in Nuremburg. The Nazis built false walls into castles. The mining system in Germany is extensive, so they also hollowed out salt and copper mines and built racks all the way around.

When the Monuments Men found stolen art, was it generally in good condition?
Early on many works were stored fairly well. But as the Nazis got more desperate in the later stages of war they were having to move not only the works they stole but also art from their own museums. Frames consume a lot of space, so paintings were literally pulled out of their frames. The Nazis were loading trucks in the open rain and putting art into damp mines. There are all sorts of cases of Monuments Men finding paintings with moss literally growing through the weave of the canvas like an old Chia Pet. Other paintings were loaded on to straw on open trucks and rattled back and forth over rickety roads. The Nazis were moving the works as the Western Allies were pummeling them from the air. Frankly, it's a miracle more paintings weren't destroyed.

Why isn't the story of the Monuments Men better known?
They weren't a big group. There were 12 Monuments Men on the ground by the time of the landings on Normandy. By the end of the war, there were fewer than 60 in the field. Most of them didn't know each other because they were just so spread out geographically. There was never a cohesive unit. They never had a patch. They were sublet to whatever army they were with. And at the end of the war I think they came back and they just got lost in the fog of history.

The Monuments Men stayed in Europe for six years after the war to finish their work. How many works did they eventually return?
By 1951 they had restituted more than 5 million objects. That includes thousands of church bells the Nazis were going to melt down and use for war materials. The main mine that contained many of the works destined for Hitler's Führermuseum had more than 10,000 paintings, sculptures and other works of art. It's unimaginable. We're not talking about average things, but sculptures by Michelangelo and paintings by Vermeer.

For the Monuments Men, was it just a matter of protecting objects from the Nazis?
They wanted to be right there where the action was so they could get in and protect our cultural heritage — and not just from the enemies. Often times a well-intentioned core of engineers would see a church in ruins, knock it down and use the material to build roads. Because of their experience with restoration, the Monuments Men realized that sometimes those churches could be salvaged. Sometimes the pieces of a fresco could be put back together. Sometimes something that looked beyond repair could be repaired and they had the sensibility to understand that.

There are still thousands of stolen works floating around in antiques shops, in people's private collections and elsewhere. Do you think they'll ever be recovered?
I think over the next 15 to 20 years many of those things that are missing will surface. As the WW II generation passes over the next five to 10 years, these things in attics and basements and on walls will pass on to younger generations, and they might try to sell them. Buyers will want to know what they are buying and where it came from — and that could lead to answers.

• William Lee Adams / London
• In his new book 'Monuments Men', Robert Edsel tells the stories of the men and women dedicated to rescuing the world's greatest artworks from the Nazis during World War II