The Rule of Equity addresses some of the issues that affect American Indians. Many of these are unique, starting with the term "American Indian," discussed below. Many they share with other Americans. Imiportant issues include:
Reservations (crime, poverty, etc.)
Societal discrimination and racism
Sports mascots and team names
Scope of sovereignty
One useful source of news involving American Indians is Indian Country Today.
Here is more detail on the controversy about terminology, borrowed from Wikipedia:
Native Americans are more commonly known as Indians or American Indians, and have been known as Aboriginal Americans, Amerindians, Amerinds, Colored, First Americans, Native Indians, Indigenous, Original Americans, Red Indians, Redskins or Red Men. The term Native American was introduced in the United States by academics in preference to the older term Indian to distinguish the indigenous peoples of the Americas from the people of India, and to avoid negative stereotypes associated with the term Indian. Some academics believe that the term Indian should be considered outdated or offensive. Many indigenous Americans, however, prefer the term American Indian. Others point out that anyone born in the United States is, technically, native to America. In this sense, "native" was substituted for "indigenous". Today, people from India (and their descendants) who are citizens of the United States are called Indian Americans or Asian Indians.
Criticism of the neologism Native American comes from diverse sources. Russell Means, an American Indian activist, opposes the term Native American because he believes it was imposed by the government without the consent of American Indians. He has also argued that the use of the word Indian derives not from a confusion with India but from a Spanish expression En Dio, meaning "in God".
Furthermore, some American Indians question the term Native American because, they argue, it serves to ease the conscience of "white America" with regard to past injustices done to American Indians by effectively eliminating "Indians" from the present. Still others (both Indians and non-Indians) argue that Native American is problematic because "native of" literally means "born in," so any person born in the Americas could be considered "native". The compound "Native American" is generally capitalized to differentiate the reference to the indigenous peoples.
A 1995 U.S. Census Bureau survey found that more Native Americans in the United States preferred American Indian to Native American. Most American Indians are comfortable with Indian, American Indian, and Native American, and the terms are often used interchangeably. The traditional term is reflected in the name chosen for the National Museum of the American Indian, which opened in 2004 on the Mall in Washington, D.C..
Recently, the U.S. Census Bureau has introduced the "Asian-Indian" category to avoid ambiguity for descendants of people from India.