In the United States, a state court has jurisdiction over disputes with some connection to a U.S. state, as opposed to the federal government. State courts handle the vast majority of civil and criminal cases in the United States; United States federal courts handle different types of cases.
Cases in state courts begin in a trial court where lawsuits and criminal cases are filed and evidence is eventually presented if a case proceeds to a hearing or trial. Trials in these courts are often held only after extensive pre-trial procedures that in more than 90% of cases lead to a default judgment in a civil case, an agreed resolution settling the case or plea bargain resolving a criminal case, or pre-trial resolution of the case by a judge either on the merits or on procedural grounds. Territory outside of any state in the United States, such as the District of Columbia or American Samoa, often have courts established under federal or territorial law which substitute for a state court system, distinct from the ordinary federal court system.
State trial courts are usually located in a courthouse in the county seat. Even when state trial courts include more than one county in a judicial district, it isn't uncommon for the state trial court to hold regular sessions at each county seat in its jurisdiction and function from the point of view of litigants as if it were a county based court.
If one of the litigants is unsatisfied with the decision of the lower court, the matter may be taken up on appeal (but an acquittal in a criminal trial may not be appealed by the state due to the Fifth Amendment protection against double jeopardy). Usually, an intermediate appellate court, if there is one in that state, 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, which is usually called the state supreme court and is usually located in or near the state capital. Appellate courts in the United States, unlike their civil law counterparts, are generally not permitted to correct mistakes concerning the facts of the case on appeal, only mistakes of law, or findings of fact with no support in the trial court record.