The deputy mayor (also known as vice mayors or sometimes even assistant mayors) is an elective or appointive office of the second-ranking official that is present in many, but not all, local governments.
Many elected deputy mayors are members of the city council who are given the title and serve as acting mayor in the mayor's absence. Appointive deputy mayors serve at the pleasure of the mayor and may function as chief operating officers.
There may be within the same municipal government one or more deputy mayors appointed to oversee policy areas together with a popularly-elected vice mayor who serves as the mayor's successor in the event the office is vacated by death, resignation, disability, or impeachment.
In other cities, the deputy mayor presides over the city council, and may not vote except to break ties. Like the deputy mayor in other systems, the popularly elected deputy mayor becomes an Acting Mayor in the original mayor's absence. As previously noted, in some few cities, this office is elected separately and does not entail the elevation by the council of one of its members to be speaker. In some U.S. cities, the mayor and deputy mayor run together as a citywide ticket similar to how the president and vice president run at the national level.
In Cincinnati, Ohio, the vice mayor is appointed by the mayor from amongst the elected city council members. As of January 2, 2018, Christopher Smitherman has served as the vice mayor of Cincinnati after being appointed by Mayor John Cranley to replace former Vice Mayor David S. Mann.
In Israel, according to the Local Authorities (Election and Term of Mayor and Deputy Mayors) Act, 5735-1975, a Mayor is usually elected in "personal, general, direct, equal and secret elections", with election by a local council being made only if no candidate runs for mayor, a candidate for mayor in a single-candidate election is rejected (in Israel, unlike in the UK, if only one candidate runs he is not automatically elected, and voters would vote either for that candidate or against him), or both candidates advancing to the runoff received an equal number of votes and the tie remains unbroken after adding the number of first-round votes cast for them with the number of second-round votes cast for them. However, deputy mayors are always elected by the local council, of which one is (or, in certain local authorities two are) the Designated Acting Mayor, elected after nomination by the Mayor.
The French term député-maire does not mean "deputy mayor", but refers to a mayor who is also a deputy of the National Assembly of France. As of 31 March 2017, a mayor cannot hold both posts (article LO 141-1 of the electoral code). The term for deputy mayor in French is Maire adjoint.
In Davao City, there is both an elected vice-mayor as a direct constitutionally mandated deputy of the Mayor of Davao City and appointed deputy mayors. The deputy mayors are appointed to administer each ethnic minorities situated in Davao City.
In Spain, this function is performed by a "Teniente de alcalde."