An interesting look at 10 different cases (some well known, some more obscure) where countries are involved in disputes over the ownership of looted cultural property. Some of the cases have been resolved, but many are still no closer to reaching a conclusion than the day after the artefacts were originally taken.
Business Insider 
10 Ancient Artifacts That Countries Are Still Fighting Over
Vivian Giang | Jul. 14, 2011, 7:51 PM
Legendary historical artifacts have traded hands from conquerors to thieves and ended up thousands of miles from their origin.
The question of ownership is extremely murky.
With a black market in looted art worth as much as $6.3 billion a year, the mantra of “finder’s keepers” can be tempting. Past and present owners, however, may claim an object, sometimes leading to disputes and wars between nations.
2003: Bombing survivors demand the University of Chicago auction off Iran’s ancient clay tablets
The surviving victims of a 1997 bombing attack in downtown Jerusalem are demanding that the University of Chicago auction off ancient clay tablets belonging to Iran to pay for the damages.
The Iranian government is responsible for training the militant group – Hamas – who carried out the bombing at the Ben Yehuda mall, injuring and fatally wounding more than 100 civilians.
The ancient tablets were originally brought to the University of Chicago in 1937 for research purposes after American archaeologists discovered the 2500-year-old artifacts in Persepolis, the former capital of the Persian Empire.
Over time, approximately 37,000 of the artifacts have been studied and returned to Irans’s Cultural Heritage and Tourism Organization and approximately 5,000 remain at the University of Chicago’s Oriental Institute Museum.
In 2003, a United States District judge in Washington awarded the group more than $250 million in damages to be paid for by the Iranian government. The survivors suggest that the remaining clay tablets be sold by the University of Chicago to pay for their awarded damages.
The University of Chicago is arguing that governments cannot be sued by ordinary citizens.
A federal court ruling prohibits the transferring of any of the artifacts until the case is adjourned.
2005: Ethiopia reunites with their Obelisk of Axum
In 2005, a 1,700-year-old stone obelisk returned to Ethiopia after 70 years in Italy.
The Axum obelisk – considered to be a part of the one of the great kingdoms of the ancient world – was looted by Italian troops in 1937.
Dismantling and sending the 160-ton obelisk back to Ethiopia cost the Italian government $7.7 million. To refrain the obelisk from freezing, heaters were installed on the planes and the monument was wrapped in steel bars to keep it from moving during the six-hour flight.
2011: Yale University gives back 40,000 artifacts to Peru ends 100-year dispute
Yale and Peru ended a 100-year bitter dispute when the university agreed to return 40,000 artifacts originally taken from the Machu Picchu site in the Andes in the early 1900s.
Peru has claimed that the ancient artifacts — pottery, jewelry and bones — were sent to Yale for 18 months in 1911 but were never returned to the country.
In 2008, Peru filed a lawsuit against Yale to return the pieces and Peru’s President sent President Obama a letter seeking his assistance in 2010.
An exhibit for the artifacts was opened to the public in April 2011 at the Government Palace in Lima.
2011: Cambodia and Thailand wage mini war over ancient temple
In Cambodia it is called Preah Vihear and in Thailand it is called Khao Phra Viharn, but both countries claim ownership of the temple at the Cambodia-Thailand border believing it is on their own land.
Ownership of the ancient, stone-walled temple has been the subject of dispute between the two countries since withdrawal of the French in the 1950s.
In a 1962 decision, the International Court of Justice gave Cambodia sovereignty of the surrounding land. Shortly thereafter, Thailand withdrew from the International Court of Justice.
Cambodia has requested that the International Court of Justice formally clarify its decision.
The mini-war resumed in 2008 when the United Nations Educational, Scientific and Cultural Organization announced the temple a World Heritage with ownership to Cambodia.
In February 2011, the United Nations ordered a ceasefire between the two nations after 10 people perished but the dispute resumed in April resulting in the deaths of 18 people and evacuation of 85,000.
Ongoing: Egypt seeks the return of their Sphinx’s beard currently stored in a basement in Britain
The Sphinx — a symbol of ancient Eygypt — is a monument built in the image of Pharaoh Khafre from the fourth dynasty.
The beard of the 4,600-year-old artifact accidentally fell off, was carted away and sold to the British Museum in 1818.
For the past 160 years, it has been stored in the basement of the museum with no plans to be returned to Eqypt.
Ongoing: The Rosetta Stone dispute between Eqypt and Britain
A black basalt stone discovered in Rosetta, Eqypt in 1799 by a french officer is still the subject of dispute between nations today.
Known as the Rosetta Stone, the famous artifact has inscriptions in ancient Greek, demotic characters and hieroglyphics. The 2,200-year-old stone is believed to hold the secret to translating hieroglyphics and Eqypt’s ancient past.
In French’s surrender to the British in 1801, the Rosetta Stone was transferred to the British Museum in London.
Eqypt has continued to seek for the stone’s return.
Ongoing: India’s Hindus and Muslims dispute over Babri mosque
In the northern state of Uttar Pradesh, Muslim clerics and leaders rallied against a court ruling over the site of a demolished mosque.
The 2010 high court ruling gave ownership of two-thirds of the land to Hindus, resulting in Muslims rejecting the verdict and appealing at the supreme court level.
Hindus and Muslims have quarreled over the Babri mosque for more than a century. Hindus claim the site is the birthplace of their god Rama.
In 1992, the Muslim mosque was demolished by Hindu mobs — the riot was considered one of the worst in India’s history, killing 2,000 people.
Ongoing: Eqypt wants 3,000-year-old statue back; Germany claims its too delicate to move
Eqypt has been conducting an ongoing campaign to get more than 5,000 artifacts from around the world that they claim belongs to them.
Their main leader is Zahi Hawass – the antiquities chief for Egypt’s Supreme Council of Antiquities – and at the top of his list is the bust of Nefertiti – which was allegedly stolen in 1913 by German archaeologists using illegal documents.
The 3,300-year-old bust is a statue of the wife the pharaoh Akhenaten, whose name was erased form monuments after his death in 1338 B.C. by priests who disapproved of his religious practices.
Germany claims that the statue is too delicate to make the long trip back to Eqypt.
Ongoing: Greece demands the return of their Elgin Marbles; the British refuse
In a dispute with the Prime Minister David Cameron, Greece asserts that the return of the Parthenon marbles to Athens could potentially alleviate the country’s current financial crisis.
The marble sculptures were given to Lord Elgin in 1799 by the Sultan of the Ottoman Empire who once controlled Greece.
Cameron has refused to move the marbles from the British Museum back to Greece
Ongoing: Native American tribes clash over burial remains
An ancient burial ground is the center of dispute between two Native American tribes who believe the land is the resting ground for their ancestors’ remains.
Archaeologists found 174 ancient Native American remains at the site believed once to have been shared by the Gabrielino-Tongva and Juaneño Band of Mission Indians in California’s Huntington Beach.
Half of the remains have been unearthed