Each state’s constitution and laws establish the state’s courts, which interpret state laws (and generally not federal laws). A court of last resort, often known as a supreme court, is usually the highest court in the state. Some states also have an intermediate court of appeals. Below these intermediate courts of appeal are the state trial courts, where most lawsuits begin. State trial courts are referred to differently in different states—often as district courts, circuit courts, or superior courts.

State courts are often courts of general jurisdiction—meaning they hear all types of cases—involving criminal law, family law, probate law, and general disputes involving money and property. But more populated counties often have courts of specific jurisdiction, such as family courts that only hear family law matters (divorce, child custody, child support); criminal courts that only hear criminal matters; and probate courts that only handle the probate of estates and related litigation.

In New York State, the court system is structured with several levels, including a court of last resort, intermediate appellate courts, and trial courts. The court of last resort is the New York Court of Appeals, which is the highest court in the state. Below the Court of Appeals are the Appellate Divisions of the Supreme Court, which serve as the intermediate appellate courts. New York's trial courts include the Supreme Court, which is a court of general jurisdiction and handles civil matters, and the County Court, which handles criminal cases outside of New York City. Within New York City, the Supreme Court handles both civil and criminal matters. There are also specialized courts, such as Family Court, which deals with family-related issues like divorce, child custody, and support, and Surrogate's Court, which handles probate and estate matters. Additionally, there are local courts such as City Courts, District Courts, and Town and Village Courts, which handle lesser civil and criminal matters. New York's court system is designed to handle a wide range of legal issues, from general disputes to specific jurisdictional matters.