Abstract: Smart health is a real-time, intelligent, ubiquitous healthcare service based on the IoT aware network and sensing infrastructure. Thanks to the rapid development of related technologies such as cloud computing, fog computing and IoT, research on smart health is gradually on the right track. This paper analyzes research on smart health in recent years and then discusses the development of smart health from both cloud and edge, including cloud computing, fog computing, IoT sensors, blockchain, and privacy and security. At present, in the research of cloud and smart health, the focus is on how to use the cloud to complete the challenges of massive health data and improve service performance, including related issues such as storage, retrieval and calculation of health big data in the cloud. At the edge, research focuses on the collection, transmission, and computation of health data, including sensors and wearable devices for collecting health data, various sensor networks, and how to process health data and improve service performance at the edge. As an emerging technology, blockchain has a wide range of applications in smart health. We discuss typical smart health application, blockchain in smart health and privacy and security issues related to smart health. Finally, we present challenges and opportunities for smart health in the edge computing era.