When two states have a controversy between each other, the case is filed for original jurisdiction with the United States Supreme Court. This is one of the very limited circumstances where the court acts as original jurisdiction, e.g. a trial court. In all other cases the court acts as the highest level appellate court in the United States.
The cases involved were all named Arizona v. California, and were decided in 1931, 1934, 1936, 1963, 1964, 1968, 1979, 1983, 1984, 2000 and 2006.
The original decision, involved the following question: How much water is Arizona entitled to under the Colorado River Compact of 1921?
Since then, the case has been relitigated several times due to disputes over California's need for more water than Arizona would like it to have.
In summary, as long as there is at least of water available from the Colorado River, California gets , Nevada gets and Arizona gets the difference. If there is more available, California has been entitled to 50% of the water from the Colorado River, Arizona is entitled to 46% and Nevada, 4%. If there is less, the Secretary of the Interior has to divide up the water according to various formulas (which is what the court cases were about) ensuring that each of the states get a certain amount of water, except that California has an absolute fixed maximum of 4.4 million acre-feet per year (547 U.S. 157). Some of the adjustments involved rights the U.S. Government had with respect to supplying water to Indian tribes pursuant to Executive Orders signed by the President of the United States as far back as 1907.