In this research, an extensive literature review was performed on the recent developments of the ambulance routing problem (ARP) and ambulance location problem (ALP). Both are respective modifications of the vehicle routing problem (VRP) and maximum covering problem (MCP), with modifications to objective functions and constraints. Although alike, a key distinction is emergency service systems (EMS) are considered critical and the optimization of these has become all the more important as a result. Similar to their parent problems, these are NP-hard and must resort to approximations if the space size is too large. Much of the current work has simply been on modifying existing systems through simulation to achieve a more acceptable result. There has been attempts towards using meta-heuristics, though practical experimentation is lacking when compared to VRP or MCP. The contributions of this work are a comprehensive survey of current methodologies, summarized models, and suggested future improvements.