Ambulance Routing Problem (ARP) is the part of Emergency Medical Services (EMS), which provide timely medical help for those who are in need. In Medical emergency situation, the key concern is, to provide early treatment. Relocating patients quickly to neighboring medical facilities is extremely difficult given the existing traffic situation and has to be rectified. A lack of EMS owing to urbanization and several routing considerations such as the precise location of the request, traffic problems, road width, and ambulance locations are few of the difficulties. This paper summarizes a number of recent studies on ARP in routing and the issues they raised. In this survey, Routing for Ambulance vehicles is categorized as initiating ambulance from depot to injured location (response Time) and routing from injured location to nearby medical Centre (Travel Time). And, we highlighted challenging issues and constraints related to route optimization in both above mentioned category. Also emphasized the less explored research area like Interfacility hospital transfer and importance of incorporating safety metrics during Ambulance Routing.