Once the Americans got into the war and started to push they managed, in true American fashion, to blow a lot of shit up. American troops were moving into territory that had a cultural history with artifacts several times older than the presence of white folk in North America. It would be quite the mental shift for the average American to think of buildings as anything other than things that could be hidden in. The whole reason the French rolled over when they were invaded was to preserve their art and architecture. A select few American art historians understood this and wanted to preserve things from the American advance.
The Monuments Men had the job of, at first, asking commanding officers to not blow up historic churches. But as their forces advanced they were also to try to reclaim stolen art and return it to it's proper owners... or their heirs... or... well, shit, that was a puzzle in many cases. Soon they found they had to get in behind enemy lines and rescue art from being destroyed during the Nazi retreat or to figure out where the Nazis hid the stolen art. And, in some cases, to keep art from being claimed by the Soviets as restitution for war losses.
In one case they discovered not just art, but tons and tons of Nazi gold. That gold was what they were using to back their claims of being able to pay back war loans. By taking that gold from the Nazis, the Monuments Men undermined a great deal of Nazi funding and accelerated the end of the war.
I'm not much of a war movie buff. But this movie I liked. They tell this largely forgotten story with humor and a minimum of gore. You can safely take your teenaged kids to see this movie. And I'll be getting it on DVD. I definitely recommend this movie.