In the last fifty years, researchers have developed statistical, data-driven, analytical, and algorithmic approaches for designing and improving emergency response management (ERM) systems. The problem has been noted as inherently difficult and constitutes spatio-temporal decision making under uncertainty, which has been addressed in the literature with varying assumptions and approaches. This survey provides a detailed review of these approaches, focusing on the key challenges and issues regarding four sub-processes: (a) incident prediction, (b) incident detection, (c) resource allocation, and (c) computer-aided dispatch for emergency response. We highlight the strengths and weaknesses of prior work in this domain and explore the similarities and differences between different modeling paradigms. We conclude by illustrating open challenges and opportunities for future research in this complex domain.