When Lord Elgin, a British aristocrat, sailed home from Greece in the early 1800s, he also shipped to England some of the greatest treasures of antiquity: a collection that included statues of Greek gods and carved frieze panels depicting battling centaurs that once decorated the Parthenon in Athens.

Torn in some cases from the temple walls, ostensibly with the permission of the Ottomans who then ruled Greece, the so-called Elgin Marbles were later sold to the British government and became some of the most storied artifacts in the collection of the British Museum.

But they also became, almost from the very day they were removed, the subject of perhaps the world’s most notorious cultural dispute.

Since the days of Lord Byron, the romantic poet who was an early critic of their removal, the fate of the marbles has been bitterly contested. The British say the marbles were legally acquired and are best shown alongside other artifacts in a universal museum, while the Greeks view them as looted treasures that are a foundation of their national heritage.

The debate has only deepened in recent years as the actions of old empires have come under new scrutiny, and restitution battles have come to challenge the foundations of Western museums. The pressure to return the marbles has grown as museums have given back high-profile items including Benin Bronzes, Italian antiquities and other fragments from the Parthenon that were relinquished just last month by the Vatican.

Now there are hopeful signals that perhaps a resolution between the British Museum and Greece could be in sight as officials on both sides have acknowledged that secret talks have taken place. But even as those disclosures have flowered into optimism that real progress will soon be made, both sides have made it clear that no deal is yet imminent.

Indeed, they remain far apart on some key questions.