Due to the complexity of this matter, many factors should be considered. Giving art to the culture that created it helps to foster a sense of pride for one’s community and history. It is also the natural decision, since they were the ones who created the given artwork. However, the fact that different cultures’ artwork is so mixed around the world exposes people to a diverse collection of art from cultures both similar and wholly different from their own. For instance, the Greek Altar of Pergamon from the Hellenistic Period is currently in a German museum.
Unfortunately, much artwork held in countries that they did not originate from is not because of cultural diversity. Rather, the artwork was seized by a conquering culture and never returned. This does not foster a global world. Instead, it limits relationships between countries and hinders international peace. Seized artwork should be returned to the home of the artwork if that is what the country wants.
There are some cultures that are now extinct. They could be assigned to the people who live in the same geographical area as them, but this is not always the fair choice. The cave paintings in France and Spain were not created by people from the modern French and Spanish culture, but they were geographically located in France and Spain. Should they, and whatever profits they generate, belong to whoever owned the land or to the government? Such questions almost always depend upon each individual situation.