Of course, such a crime as stealing Mona Lisa is considered the greatest art theft of the 20th century. It made Vincenzo Peruggia a world-famous thief. He hid the legendary painting in his apartment in Paris and threw dust into the eyes of the police: they accepted his alibi that he had been working at a different location on the day of the theft. This way, Joconde had been hidden in his apartment for... two years!
Peruggia was an Italian thief, and later he returned to Italy with his famous trophy. He kept it in Florence, but wasn't so careful that time: the thief was finally caught when he contacted Alfredo Geri, the owner of an art gallery in Florence, Italy. Geri's story conflicts with Peruggia's, but it was clear that Peruggia expected a reward for returning the painting to what he regarded as its "homeland."
I recommend reading more into this amazing story if ever you have the chance. There is also a documentary about this occurrence. The theft made the Mona Lisa famous, as not many people were aware of it before.