The supreme court of each state is the final authority on the interpretation of that state's laws and constitution. A case may be appealed from a state court to the U.S. Supreme Court only if there is a federal question (an issue arising under the U.S. Constitution, or laws/treaties of the United States). The relationship between federal and state laws is quite complex; together, they form the U.S. law.

The federal judiciary consists of the U.S. Supreme Court, whose justices are appointed for life by the President and confirmed by the Senate, and various "lower" or "inferior courts," among which are the courts of appeals and district courts.

The first Congress divided the nation into judicial districts and created federal courts for each district. From that beginning has evolved the present structure: the Supreme Court, 13 courts of appeals, 94 district courts, and two courts of special jurisdiction. Congress retains the power to create and abolish federal courts, as well as to determine the number of judges in the federal judiciary system. It cannot, however, abolish the Supreme Court.

There are three levels of federal courts with general jurisdiction, meaning that these courts handle criminal cases and civil law suits between individuals. The other courts, such as the bankruptcy courts and the tax court, are specialized courts handling only certain kinds of cases. The bankruptcy courts are branches of the district courts, but technically are not considered part of the "Article III" judiciary because their judges do not have lifetime tenure. Similarly, the tax court is not an Article III court.

The U.S. district courts are the "trial courts" where cases are filed and decided. The United States courts of appeals are "appellate courts" that hear appeals of cases decided by the district courts, and some direct appeals from administrative agencies. The Supreme Court hears appeals from the decisions of the courts of appeals or state supreme courts (on constitutional matters), as well as having original jurisdiction over a very small number of cases.

The judicial power extends to cases arising under the Constitution, an Act of Congress, or a U.S. treaty; cases affecting ambassadors, ministers, and consuls of foreign countries in the U.S.; controversies in which the U.S. government is a party; controversies between states (or their citizens) and foreign nations (or their citizens or subjects); and bankruptcy cases. The Eleventh Amendment removed from federal jurisdiction cases in which citizens of one state were the plaintiffs and the government of another state was the defendant. It did not disturb federal jurisdiction in cases in which a state government is a plaintiff and a citizen of another state the defendant.

The power of the federal courts extends both to civil actions for damages and other redress, and to criminal cases arising under federal law. Article III has resulted in a complex set of relationships between state and federal courts. Ordinarily, federal courts do not hear cases arising under the laws of individual states. However, some cases over which federal courts have jurisdiction may also be heard and decided by state courts. Both court systems thus have exclusive jurisdiction in some areas and concurrent jurisdiction in others.

The Constitution safeguards judicial independence by providing that federal judges shall hold office "during good behavior". Usually they serve until they die, retire, or resign. A judge who commits an offense while in office may be impeached in the same way as the President or other officials of the federal government. U.S. judges are appointed by the President and confirmed by the Senate. Another Constitutional provision prohibits Congress from reducing the pay of any judge. Congress could enact a new lower salary applying to future judges, but not to those already serving.