Physical sensors, intelligent sensors, and output recommendations are all examples of smart health technology that can be used to monitor patients’ health and change their behavior. Smart health is an Internet-of-Things (IoT)-aware network and sensing infrastructure that provides real-time, intelligent, and ubiquitous healthcare services. Because of the rapid development of cloud computing, as well as related technologies such as fog computing, smart health research is progressively moving in the right direction. Cloud, fog computing, IoT sensors, blockchain, privacy and security, and other related technologies have been the focus of smart health research in recent years. At the moment, the focus in cloud and smart health research is on how to use the cloud to solve the problem of enormous health data and enhance service performance, including cloud storage, retrieval, and calculation of health big data. This article reviews state-of-the-art edge computing methods that has shifted to the collection, transmission, and calculation of health data, which includes various sensors and wearable devices used to collect health data, various wireless sensor technologies, and how to process health data and improve edge performance, among other things. Finally, the typical smart health application cases, blockchain’s application in smart health, and related privacy and security issues were reviewed, as well as future difficulties and potential for smart health services. The comparative analysis provides a reference for the the mobile edge computing in healthcare systems.