Loot or heritage?

Greek Prime Minister Kyriakos Mitsotakis called on the British Museum to return ancient Greek treasures, the Parthenon Sculptures, during an interview with the BBC while visiting the UK. Similar disputes over the restitution of looted artifacts by former colonizers or invaders to their countries of provenance have been going on for years. China has also been calling on the return of stolen artifacts from Western museums, but without much avail. What are the hurdles including legal ones in the process?