Italian police just announced seizing "5,361 vases, kraters, bronze statues and frescoes valued at some 50 million euros" from an art dealer in Switzerland. Lots of illegal digging going on in Italy.
What happens to these objects now? No museum in Italy has room to display them, so I suppose they will disappear into some heavily guarded government warehouse. I have a suggestion: how about organizing them as a traveling exhibit that would visit places like Montana, Manitoba, Costa Rica and Kenya where people don't get to see much classical stuff? Billing them THE STOLEN CLASSICS or LOOT or some such ought to draw in the visitors.