Tribes are sovereign governments and have exclusive inherent jurisdiction over their territory and members, but not necessarily jurisdiction over non-Indians even within tribal territory. Tribes are under the exclusive and plenary jurisdiction of the federal congress, which may restrict or abolish jurisdiction and sovereignty. The federal government has exercised this power a number of times to limit tribal jurisdiction, assume federal jurisdiction over a number of areas, and delegate that jurisdiction to some states. Congress has granted limited jurisdictional authority to the federal courts (under the General Crimes Act 18 USC § 1153 and the Major Crimes Act 18 USC § 1152) and to state courts (for example under Public Law 280). Congress has imposed limits on tribal courts through the Indian Civil Rights Act (ICRA 25 USC § 1301-1303).
For more information, please visit the Judicial Council of California’s Tribal Court-State Court Forum website and their publication, "Jurisdictional Issues in California Regarding Indians and Indian Country," May 2015. https://www.courts.ca.gov/documents/Jurisdiction_in_California_Indian_Country.pdf