Recently, wearable devices have got increasing popularity in wide applications in medical and disaster rescue efforts to ensure the health and safety of users, which facilitates the development of the Internet of Medical Things (IoMT). Due to the posture alteration and mobility of users, the topology of the IoMT changes frequently, which increases the difficulty for resource allocation and routing strategy. In this paper, we respectively probe into the health monitoring architectures of the IoMT for both individual and group, allowing the monitored users to move at will. Furtherly, combined with the diversity of disaster rescuers, we build an IoMT-based disaster rescuer health monitoring system with searchers, doctors and porters. For each application, we point out the enabling technologies and demonstrate the existing researches. It is worth noting that the complexity of environment and high mobility of rescuers increase the probability of route breakage. Thus, this paper creatively addresses effective routing repair solutions for route breakage in IoMT-based disaster rescuer health monitoring system by exploiting the mobility of rescuers. Finally, we forecast three most likely directions in the field of IoMTs. INDEX TERMS IoMT, health monitoring, individual, group, disaster rescuer.