For Indian tribes, the mechanism of recognition was treaties. Treaties are a contract between governments. When two governments enter into a treaty with each other, that means they are recognizing each other as sovereigns. For example, states generally enter into contracts with each other that are called compacts. Recently, tribes have also begun to enter into compacts with states to establish casino gaming.
Treaties are the basis of the relationship between tribes and the United States.
When the United States government recognized tribes as sovereigns through treaties, they were following in the footsteps of European nations that had done the same thing. The Europeans had two very good reasons for entering into treaties with Indian tribes. First, tribes had significant military power. Until around 1800, tribes if they had united had enough military power to run Europeans off this continent. After 1800, the growing masses of white people in the East, coupled with changes in military technology, changed this situation.