With the booming development of medical informatization and the ubiquitous connections in the fifth generation mobile communication technology (5G) era, the heterogeneity and explosive growth of medical data have brought huge challenges to data access, security and privacy, as well as information processing in Internet of Medical Things (IoMT). This article provides a comprehensive review of how to realize the timely processing and analysis of medical big data and the sinking of high-quality medical resources under the constraints of the existing medical environment and medical-related equipment. We mainly focus on the advantages brought by the cloud computing, edge computing and artificial intelligence technologies to the IoMT. We also explore how to rationalize the use of medical resources and the security and privacy of medical data, so that high-quality medical services can be provided to patients. Finally, we discuss the current challenges and possible future research directions in the edge-cloud computing and artificial intelligence related IoMT. INDEX TERMS Internet of medical things (IoMT), deep learning, edge of computing, computation offloading.