Under the laws of the United States, most disputes are properly taken to the courts of the state in which the dispute arose. Disputes are heard and evidence presented in a district court, usually located in a courthouse in the county seat.

If one of the litigants is unsatisfied with the decision of the lower court, the matter may be appealed (except that an acquittal in a criminal trial may not be appealed. The highest appellate court is usually called the state supreme court. There is usually an intermediate appellate court, often called the state court of appeals. (In New York, however, the Court of Appeals is the highest state court, and the State Supreme Court, Civil Court, and Criminal Court collectively are the lowest courts.)

There is usually a county court which hears criminal arraignments and tries petty matters. Cities often have city courts which hear traffic offenses and violations of city ordinances.

The relationship between state courts and federal courts is quite complicated. Although the federal Constitution and federal laws override state laws, it is not the case that state courts are subordinate to federal courts, rather they are more accurately two sets of parallel courts. With regard to an interpretation of a state law, all Federal courts must defer to the interpretation of the state courts. A case can be moved from a state court to a Federal court only under two conditions. The first is if the case involves federal law or the U.S. Constitution. The second is if the case is between persons of different states. In the latter case, a litigant can bring a matter either to state court or federal court, and deciding on the jurisdiction is part of litigation strategy.

The United States Supreme Court sometimes accepts appeals of cases from state courts, if the justices believe that the case involves a federal question. Appeals to the federal courts from state courts are frequent in the case of death penalty cases in which a federal court is asked to review whether a defendant has been given due process of law.