Emergency response to incidents such as roadway accidents is one of the most pressing problems faced by communities across the globe. In the last fifty years, researchers have developed statistical, analytical, and algorithmic approaches for designing emergency response management (ERM) systems. In this survey, we present models for incident prediction, resource allocation, and dispatch concerning urban emergency incidents like roadway accidents and crashes. We highlight the strengths and weaknesses of prior work in this domain and explore the similarities and differences between different incident types. Finally, we present future research directions. To the best of our knowledge, our work is the first comprehensive survey that explores the entirety of ERM systems.