In Virginia, the State Board of Elections is responsible for overseeing election administration statewide. It must ensure (1) uniformity in the “practices and proceedings;” and (2) the “legality and purity in all elections.” Va. Code § 24.2-103(A). They do this through coordination, training, and issuing rules and regulations, and supplemental guidance. Va. Code § 24.2-103(A)-(D). Many of these actions, such as issuing additional guidance and developing training, are implemented through the Virginia Department of Elections, headed by the Commissioner of Elections. Va. Code Ann. § 24.2-103(H).
Local (City and County) Electoral Boards are required to follow the rules and guidance of the State Board. The State Board also provides oversight of Electoral Boards and Registrars, including the power to remove Electoral Board members and refer violations of election law to the Attorney General for investigation and enforcement. Va. Code §§ 24.2-103(E), 104(B). Due to the centralized structure of election management in Virginia, the discretion of local offices is mostly limited to administrative issues, such as choosing the location of central absentee processing or when to start preprocessing (from a date range set by statute).
See a complete overview of the officers and personnel here: