Emergency vehicle service is one of the most important public services. It plays a vital role in saving people's lives and reducing the rate of mortality and morbidity. In the past a few decades, intensive efforts have been devoted by researchers to design effective and efficient strategies to ensure the quality of the service of emergency vehicles under different environments. This study seeks to provide a holistic review of the models and strategies designed in literature to improve the emergency vehicle service. According to the steps of an emergency vehicle to response to a call demand, this study identifies four problems in the field of the emergency vehicle service, i.e., the location problem, the dispatching problem, the routing problem, as well as the preemption control problem. We will review the past studies devoted to addressing each problem explicitly. This review can help the interested reader to trace the evolution of the models and current keen research interests in the field of emergency vehicle service.