Answer
Tribes possess all powers of self-government except those relinquished under treaty with the United States, those that Congress has expressly extinguished, and those that federal courts have ruled are subject to existing federal law or are inconsistent with overriding national policies. Tribes, therefore, possess the right to form their own governments; to make and enforce laws, both civil and criminal; to tax; to establish and determine membership (i.e., tribal citizenship); to license and regulate activities within their jurisdiction; to zone; and to exclude persons from tribal lands.
Limitations on inherent tribal powers of self-government are few, but do include the same limitations applicable to states, e.g., neither tribes nor states have the power to make war, engage in foreign relations, or print and issue currency.
