The occurrence of any kind of natural disaster will eventually lead to the loss of life and property. Countries where such disasters occur make every effort to monitor such disasters and aid as quickly as possible. However, in some cases, a rescue cannot be sent because no information is available to initiate any type of rescue operation. This is usually because common disaster management systems (DMS) use on board or ground networks to route information from the disaster scene to rescue headquarters (HQ), which in most cases cannot provide the information efficiently. One effective approach is to use satellites in conjunction with existing air-to-ground systems. This study provides a comprehensive and systematic overview of the complexities of the space-air-ground integrated network (SAGIN) in disaster management applications, including different architectures and protocols. The main rationale behind this review is to provide an extensive analysis of existing disaster management systems that are making use of SAGIN. This paper also presents the taxonomy for disaster management systems and challenges. Moreover, this research work also highlights open research issues and challenges for any type of disaster scenario. Our results indicate that several challenges are faced by disaster management systems such as hardware-based challenges, network-based characteristics and communication protocols related challenges, availability and accuracy of imagery data, and security and privacy issues.