Emergency situations encompassing natural and human-made disasters, as well as their cascading effects, pose serious threats to society at large. Machine learning (ML) algorithms are highly suitable for handling the large volumes of spatiotemporal data that are generated during such situations. Hence, over the years, they have been utilized in emergency management to aid first responders and decision-makers in such situations and ultimately improve disaster prevention, preparedness, response, and recovery. In this survey article, we highlight relevant work in this area by first focusing on the commonalities of emergency management applications and key challenges that ML algorithms need to address. Then, we present a categorization of relevant works across all the emergency management phases and operations, highlighting the main algorithms used. Based on our review, we conclude that ML algorithms can provide the basis for tackling different activities across the emergency management phases with a unified algorithmic framework that can solve a large set of problems. Finally, through the systematic literature review, we provide promising future directions for utilizing ML algorithms more effectively in emergency management applications. More importantly, we identify the need for better generalization of algorithms, improved explainability, and trustworthiness of ML algorithms with respect to the emergency management personnel, as well as more efficient ways of addressing the challenges associated with building appropriate datasets.