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 trial 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 taken on appeal (but an acquittal in a criminal trial may not be appealed due to the Fifth Amendment protection against double jeopardy). An intermediate appellate court, often called the state court of appeals, will review the decision of the trial court. If still unsatisfied, the litigant can appeal to the highest appellate court in the state, usually called the state supreme court. (In New York, however, the Court of Appeals is the highest state court, and the Supreme Court, Civil Court, and Criminal Court collectively are the lowest courts.)

Many states have an court of inferior jurisdiction, presided over by a magistrate or justice of the peace who hears criminal arraignments and tries petty offenses and small civil cases. 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 certain conditions; typically, these "removed cases" involve disputes arising under federal law, or lawsuits between persons residing in different states. In either circumstance, the plaintiff can bring a matter either to state court or federal court; if the plaintiff files suit in state court, the defendant often can remove the case to federal court. Deciding on the jurisdiction is part of litigation strategy for both plaintiff and defendant.

The United States Supreme Court will sometimes accept an appeal from a state's highest appellate court, if the justices believe that the case involves an important question of Constitutional law or federal law.

Another method of federal court review of state court judgments in criminal cases is the federal writ of habeas corpus, in which a federal court is asked to review whether a defendant has been given due process of law. If the federal court finds that the defendant has been denied due process then the defendant must be released or re-tried in the state court. Applications for habeas corpus review are most frequently made in death penalty cases, although the scope of review has been sharply restricted in recent years by Supreme Court decisions and legislation.

Nomenclature

The following table notes the names of the courts in the states and territories of the United States. Listed are the principal courts of first instance (general jurisdiction), the principal intermediate appellate courts, and the courts of final appeal. Most states also have several courts of limited jurisdiction (mayor's courts, magistrate's courts, county courts, municipal courts, courts of claims, etc.), which are not listed here. In some cases where courts are generally assigned to counties, the number of county-based courts does not exactly match the number of actual counties in the state. This happens when a single court has jurisdiction over more than one county.

It is notable that Delaware and Tennessee still make a distinction between a court of law and a court of equity (chancery court). For the most part in the American legal system, while the distinction between law and equity has some legal consequences, separate court systems are not maintained.