General Court (1777-1851) - The General Court existed prior to the American Revolution as the principal court, and the only appeal court in the colony. During its existence, the court sat at the state capitol. It had original jurisdiction in nearly all types of cases, and appellate jurisdiction from all of the lower courts. After statehood, the General Court was reestablished by an act of assembly in October 1777. After the war, however, its functions were reduced. When the District Courts were established in 1789, they were given appellate jurisdiction over the county courts in common law cases and the High Court of Chancery acquired similar jurisdiction in chancery cases. The General Court was therefore left with concurrent jurisdiction chiefly in civil cases connected with public debtors, probate of wills and granting of administrations, recordation of deeds, and appellate jurisdiction in criminal cases. By an act of the General Assembly passed in February 1814, the option of recording a property deed in the General Court ceased. Afterwards, these instruments were required to be recorded in the county or corporation court in the jurisdiction where the property being conveyed was located. Also in 1814, the General Court was made the sole supreme criminal tribunal in the state. It continued as such until its abolition by the state constitution of 1851. It ceased to exist on 1 July 1852. When it was abolished, records were transferred to either the Supreme Court of Appeals in Richmond or the Circuit Court of the City of Richmond, depending on the type of record involved. Both were located in the State Court House and were consequently destroyed by the evacuation fire in 1865.
[Supreme] Court of Appeals (1779-present) - The Supreme Court of Appeals was created by an act of the General Assembly passed at the May 1779 session. A previous act attempting to create the court during the October 1778 session, appears to have been ineffectual. The court continues to the present day. The Court has concurrent jurisdiction in issuing and hearing writs of habeas corpus, mandamus, and prohibition (i.e. injunction). Its jurisdiction is almost exclusively appellate. Since its creation, the Supreme Court of Appeals has had final jurisdiction in civil cases. Prior to 1851 it had no criminal jurisdiction. Its jurisdiction was extended to include criminal cases when the General Court was abolished by the Constitution of 1851. Then the Supreme Court of Appeals became the state's only court of final appeals, both civil and criminal.
High Court of Chancery (1777-1802) - The High Court of Chancery was created by an act of the General Assembly passed at the October 1777 session. It eventually took over the chancery suits then pending in the General Court and was given jurisdiction in all chancery cases, whether brought before it by original process, by appeal from a lower court, or by any other legal means. Appeals from the High Court of Chancery were made to the Supreme Court of Appeals. The High Court of Chancery met at the state capitol and had jurisdiction over the entire state. The High Court of Chancery was abolished by an act of the General Assembly passed 23 January 1802 and was replaced by the Superior Courts of Chancery. Apparently, the original records of this court were destroyed when the old State Court House in Richmond was burned in 1865.
Source: “The Virginia State Court System, 1776-[the present]: A Preliminary Survey of the Superior Courts of the Commonwealth with notes concerning the present location of the Original Court Records and Published Decisions,” by Thomas Jefferson Headlee, Jr. Virginia State Library, 1969.