I'll be able to cover a small part of this, American-Indian/Native American/Indigenous/Tribal artifacts in the US. I went to school for archaeology, have done archaeological field work and have done work combating looting of artifacts.

The Native American Graves Protection and Repatriation Act (NAGPRA) is the cornerstone of protecting these kinds of artifacts and burial grounds. It makes it illegal to own or store items of ritual, burial, or human remains without permission of the relevant tribe. It mandated the return of these items to their respective tribes. It also protects American-Indian burial sites from exploitation. And while there have been some divisive actions regarding this act, such as the Kennewick Man fiasco, the act was a watershed in spreading Federal support for protecting archaeological sites and artifacts. In fact, today, it is illegal to loot, or even disturb archaeological sites or artifacts on all Federal and most State lands. (Theoretically, but there are some grievous exceptions, but 20-year rule).

With NAGPRA and the surrounding legislation working as it should quite a lot of artifacts have been returned to tribes. However, many artifacts are still in private collections, or from a private collection and lent to a museum for display. Things like arrowheads cannot be repatriated under NAGPRA so these artifacts remain in private collections. On top of that, this is a legal grey area and depending on where you are in the US it is, to varying levels, legal to loot certain artifacts from sections of private property.

Many families throughout the US will have collections of artifacts. Not all are nefariously collected. Quite a few of these collections are comprised of "I saw this on my walk at it looked neat." These looters are easily combated with educational-outreach. But other families and organizations will have historical items bought off of the market, collected in face of laws and regulations or even historical items that were collected through the process of conquest and colonization of the American-Indians. Many of these private collections are held in spite of American-Indian wishes.

In addition, there is a huge black market for artifacts and looting is both incredibly lucrative and difficult to prosecute on a smaller scale. Small scale looters are difficult to catch, due to the prevalence of private collections, and the fact that many judiciaries struggle to successfully prosecute (I know this first hand). Large scale black market looters and purchasers like (20 year rule) can lead to funding to notorious organizations and causes like (20 year rule).

So, with all that together, how an artifact came to be on display, how it was collected, who it's purchase funded if it was bought, and if it is there at the wishes of the Tribe it is most closely related to are all huge ethical questions. Because ultimately, as someone of European descent, these items don't culturally belong to me in any way. Therefore I shouldn't try to claim ownership of the cultural knowledge they contain.

P.S. There are very very relevant issues regarding the repealing of legislation in the US and legalization of looting on public lands but these are all within the past few years, so again 20 year rule.