Describing the "checkerboard" effect of legal jurisdiction over American Indians living on reservations currently operative under Federal, state, and local laws, this document presents a brief synthesis of the legislative history leading up to Public Law (PL) 83-280 and the Indian Self Determination Act of 1975 (PL 93-638). Specifically, this document addresses: early establishment of tribal sovereignty (the 1789 Northwest Ordinance, the 1834 Act of Congress, the case of Ex Parte Crow Dog, and the enabling acts of states) and the erosion of tribal sovereignty (1885 Major Crimes Act and the 1887 General Allotment Act); The Termination Act of 1953 and 1953 PL 83-280 (seen as an attempt by the U.S. government to end its responsibility to Indian peoples, since this law transferred civil and criminal law enforcement jurisdiction from the Federal government to the various states); the 1968 Indian Civil Rights Act (consent of tribes became mandatory for the assumption of further state jurisdiction); the 1975 Indian Self-Determination and Educational Assistance Act (recognized the right of tribes to manage their own affairs); the Indian Law Enforcement Act of 1975 (recent attempts to secure sovereignty based on the principle of local option repeal of PL 83-280); and Washington State under PL 83-280 (an illustration of the checkerboard effect of multiple jurisdiction). (JC)