The prestigious New York Museum of Metropolitan of Art made headlines earlier this month when museum officials announced plans to return two large statues to Cambodia, after concurring with evidence provided by Cambodian officials that the artifacts were looted from an ancient temple in the country. The Met maintains that, for now at least, the rest of their vast collection will stay put. "There are no claims at all to speak of in the antiquities field," Harold Holzer, a senior spokesperson for the Met, told The Verge. But the incident raises a thorny question for museums in the US and Europe: how many of the objects in their collections were stolen or acquired illegally, and how many should be sent home?

For now, there’s no easy answer. The process of identifying museum objects that were stolen, and then returning them to their countries of origin, is called "repatriation." While the term describes restoring something to its point of origin, it’s also been used to describe sending prisoners of war back home. In more than one sense, that’s appropriate for museum artifacts, given that many famous works — like the Greek "Elgin Marbles" at the British Museum and "Priam’s Treasure" at the Pushkin Museum in Russia — were taken from their home countries by occupying armies or grabby colonial governments, mostly over the past 300 years.

Many of these objects were also looted by people within the countries of origin. But no matter who took them, they were often spirited away across several borders and then purchased by a series of private collectors. Those individuals later sold them to museums for vast sums, maintaining that the objects were legally acquired. This makes it difficult to pinpoint the true origins of artifacts or the validity of claims to ownership. Indeed, the Archaeological Institute of America, a nonprofit group representing archaeologists in the US, estimates that as many of 85-90 percent of "classical and certain other types of artifacts on the market do not have a documented provenance."

The contention that Western museums should identify and return such objects has only come up relatively recently, over the past 50 years, namely as European and American colonies in Africa and Asia have declared independence, developed their economies, and started to throw political weight around. "Repatriation has become a hot topic in the last decade or so, with many third-world countries trying to assert their independence and cultural identity by demanding the return of their cultural objects that were stolen from them," Julia Fischer, a professor of art history at Georgia Southern University, wrote in an email to The Verge. "In many cases, I believe these objects should be returned home."

But it’s unclear how many objects in museums around the world should even be considered for repatriation, given that no clear criteria exist to make that determination. The UN has made some progress, establishing a 1970 convention designed to curb the export of stolen artifacts and allow countries to issue repatriation claims, then pay to have the objects returned. But many museums around the world have interpreted this convention to mean that if they can prove an object left its country of origin before 1970, they’re in the clear.

Meanwhile, a UN report issued last year evaluating the effectiveness of the convention found it to have "serious weaknesses," including a lack of staffing and few international laws to back it up. A UN committee established following the convention has presided over just six cases of successful restitutions in the past 40 years. But on the plus side, the United Nations Educational, Scientific and Cultural Organization (UNESCO) and international law group Interpol maintain watch lists for artifacts reported stolen. "Of course every museum director watches these things," Holzer said of the lists.

Outside of the UN and Interpol, several other efforts exist to cut down on the theft of artifacts and promote the return of stolen ones. The International Council of Museums (ICOM), a private organization representing 20,000 museums around the the globe, states in its ethics code for acquisitions that if a museum "has reason to doubt" the legality of an object, it should reach out to police and scholars to investigate the object’s country of origin. But ICOM’s leaders have also resisted the idea of a broad review of artifacts at member museums, saying in 2002: "Repatriation of objects is an issue that should be very carefully dealt with. Wise and thoughtful judgement is necessary. Unnecessarily strong judgements or declarations should in any case be avoided."

Around the same time, ICOM also began advocating something of a partial fix, an idea it calls "digital repatriation" or "virtual repatriation" — scanning and uploading images of objects online, with the intent of allowing people in origin countries the opportunity to view them without museums having to send them back. But ICOM denies that this idea is meant to replace physical object returns. In 2007, the ICOM ethics committee chair said digital repatriation "has never been proposed as a ‘soft option’ or easy alternative to physical repatriation."

Among American museums, repatriation has mostly occurred on a "case-by-case" basis — typically when officials are confronted by foreign governments with solid evidence. The process often takes years, and it isn’t pleasant. The J. Paul Getty museum near Malibu, California, infamously agreed in 2007 to return upwards of 40 artifacts to Italy, including a large statue thought to be a likeness of the goddess Aphrodite that it purchased for $18 million in 1988. In recent years, museums across the country, from Brooklyn to Arizona, have all agreed to return objects to other countries or to native tribes within the US, in part motivated by a 1990 law requiring federally-funded institutes to identify and return Native American objects.

The Met itself has repatriated dozens of objects over the past 20 years to countries including Rome, Egypt, and India, as the museum itself openly asserts, even sending The Verge press clippings of notable repatriations it has made going back to 1994. "We returned items by making good decisions on our own," said Holzer. "We have acted responsibly on a whole range of items. I can say that the Met never stops studying and researching the pieces in its collections."

But because so many museums in the US act of their own accord to return objects, there’s no sense of how many total objects have been returned so far. The Association of Art Museum Directors (AAMD), of which the Met and some 220 other museums are members, "does not keep statistics on repatriation claims or returns," as a spokesperson told The Verge. Another US museum organization, the American Alliance of Museums (AAM), also doesn't maintain any cumulative list. "The universe of US museums is vast and diverse, ranging from great institutions like the Met to the smallest college or community art galleries," said Erik Ledbetter, who led repatriation issues for AAM from 2003 to 2009. "Collecting reliable statistics from such a vast and diverse field is correspondingly hard."

It’s also difficult to say just how many more repatriation claims will pop up in the future, as countries and tribes gain more political and economic clout. Even advocates of repatriation say the practice could go too far, leaving prestigious Western museums wiped out. "I worry that with all the returns occurring lately that our museums will lack the diversity that is needed to understand world art in its entirety," Fischer said.

The AAMD says it’s not worried about this possibility, because it only focuses on repatriation claims from 1971 onward. "This does not open up all museum collections to claims," the organization’s spokesperson told The Verge. "Rather, it focuses on a limited and specific collection of materials." Officials with the Met agree. "We’re not trying to make any statements about the collection overall. There’s no purge, there’s no task force, no wholesale reexamination of things," Holzer said. Further, he argues that museums may actually help the process of returning artifacts to their home countries. "If anybody has anything to say about [objects], they can come up front and tell us," Holzer said. "If they are in the hands of private collectors or hoarders, nobody would know."