By the latter part of the 19th century, most of the American Indians had moved onto lands set aside for them (whether by force, coercion, or "voluntarily"). But the "Indian problem" still remained. They were still united tribally and culturally and resisted giving up their land, culture, and values.
In 1884, the Court of Indian Offenses was established so that Indians could deal with crimes that took place on their own land (which was, ostensibly at least, "sovereign" within US territory). One year later, the Major Crimes Act was passed, ceding authority over certain "serious" crimes to the United States for processing and prosecution. While this might be seen as understandable from the viewpoint of a "paternal" nation over its internal subordinate nation(s), it further weakened Indian authority over themselves and their land.
Later, after the institution of the General Allotment Act ( Dawes Act, 1887 and 1891 amendment), those Indians who conceded to the allotment-parceled acreage (which was put into a "trust" that after 25 yearsin 1906, the period was amended to the Secretary of the Interior's "discretion"and proof of having become "civilized, would be considered fully owned by the Indian) were no longer under the jurisdiction of the Indian Court of Offenses and subject the all state, civil, and federal law (rather than only cases of serious crimes)this was tied in with the "reward" of citizenship granted the allotment Indian following the trust period.
Again, this weakened the tribal structure and bonds, aiding in the hoped for shift from "savage" to "civilized" (since it was their "primitive" culture and values holding them back), which was desiredby those genuinely trying to help and those more cynicalas part of the policy shift from removal to reservations (and/or extermination) and "assimilation," meant to "kill the Indian and save the man." Thus transforming them from Indians to Americans (the presumption being without any damage despite the destruction and devastation being done to their cultural identity and unity). As they became one with (white) civilization, there would be no need for separate courts or jurisdictions, nor for separate lands (part of the intention of the Dawes Act: parcel off the tribal land to individual Indians, and buy or sell/lease off whatever remained).
The Dawes Act was later seen as a failure. Though terribly destructive to the Indians as a culture and a people and largely responsible for the loss of millions of acres (for many non-Indians, it was quite lucrative), the tribes managed to survive. They didn't break apart into small families of American farmers, giving up their culture for the one being pushed upon them (though many did to some extent, leaving many "cultureless" and without a solid identity between two cultures, to neither of which they really belonged). Even a blanket grant of citizenship to all Indians in US territories (Indian Citizenship Act; many had already become citizens by then, anyway) did not assimilate the Indian (nor did the indoctrination and sometimes abuse in the boarding school system or the earlier discouragement and even banning of some Indian cultural/religious practices on the reservations).
Today, the Major Crimes Act still exists as part of the US Code, albeit updated and modified somewhat. Below is the original act, followed by the relevant sections prefaced by the definition of "Indian country" being used.
Mar. 3, 1885. | 23 Stat., 362.
An act making appropriations for the current and contingent expenses of the Indian Department, and for fulfilling treaty stipulations with various Indian tribes for the year ending June thirtieth, eighteen hundred and eighty-six, and for other purposes.
Be it enacted, &c. * * * That immediately upon and after the date of the passage of this all Indians, committing against the person or property of another Indian or other person any of the following crimes, namely, murder, manslaughter, rape, assault with intent to kill, arson, burglary, and larceny within any Territory of the United States, and either within or without an Indian reservation, shall be subject therefor to the laws of such Territory relating to said crimes, and shall be tried therefor in the same courts and in the same manner and shall be subject to the same penalties as are all other persons charged with the commission of said crimes, respectively; and the said courts are hereby given jurisdiction in all such cases;
And all such Indians committing any of the above against the person or property of another Indian or other person within the boundaries of any State of the United States, and within the limits of any Indian reservation, shall be subject to the same laws, tried in the same courts and in the same manner, and subject to the same penalties as are all other persons committing any of the above crimes within the exclusive jurisdiction of the United States. [March 3, 1885.]
From the United States Code, Title 18 ("Crimes and Criminal Procedure"), Part I ("Crimes"), Chapter 53 ("Indians"). [As of 23 January 2000]
US Code : Title 18, Section 1151
Sec. 1151. Indian country defined
Except as otherwise provided in sections 1154 and 1156 of this title, the term ''Indian country'', as used in this chapter, means
all land within the limits of any Indian reservation under the jurisdiction of the United States Government, notwithstanding the issuance of any patent, and, including rights-of-way running through the reservation, (b) all dependent Indian communities within the borders of the United States whether within the original or subsequently acquired territory thereof, and whether within or without the limits of a state, and (c) all Indian allotments, the Indian titles to which have not been extinguished, including rights-of-way running through the same.
US Code : Title 18, Section 1152
Sec. 1152. Laws governing
Except as otherwise expressly provided by law, the general laws of the United States as to the punishment of offenses committed in any place within the sole and exclusive jurisdiction of the United States, except the District of Columbia, shall extend to the Indian country.
This section shall not extend to offenses committed by one Indian against the person or property of another Indian, nor to any Indian committing any offense in the Indian country who has been punished by the local law of the tribe, or to any case where, by treaty stipulations, the exclusive jurisdiction over such offenses is or may be secured to the Indian tribes respectively.
US Code : Title 18, Section 1153
Sec. 1153. Offenses committed within Indian country
(a) Any Indian who commits against the person or property of another Indian or other person any of the following offenses, namely, murder, manslaughter, kidnapping, maiming, a felony under chapter 109A, incest, assault with intent to commit murder, assault with a dangerous weapon, assault resulting in serious bodily injury (as defined in section 1365 of this title), an assault against an individual who has not attained the age of 16 years, arson, burglary, robbery, and a felony under section 661 of this title within the Indian country, shall be subject to the same law and penalties as all other persons committing any of the above offenses, within the exclusive jurisdiction of the United States.
(b) Any offense referred to in subsection (a) of this section that is not defined and punished by Federal law in force within the exclusive jurisdiction of the United States shall be defined and punished in accordance with the laws of the State in which such offense was committed as are in force at the time of such offense.
[Note: 109A deals with "Sexual Abuse;" 1365 concerns "Malicious Mischief," specifically " Tampering with consumer products;" 661 Concerns "Embezzlement and Theft," specifically "Within special maritime and territorial jurisdiction."]
(Sources: Carl Waldman Atlas of the North American Indian, rev. ed., 2000, Major Crimes Act from http://digital.library.okstate.edu/kappler/vol1/html_files/SES0032.html, US Code material from www4.law.cornell.edu/uscode)