Medical Internet of Things, also well known as MIoT, is playing a more and more important role in improving the health, safety, and care of billions of people after its showing up. Instead of going to the hospital for help, patients’ health-related parameters can be monitored remotely, continuously, and in real time, then processed, and transferred to medical data center, such as cloud storage, which greatly increases the efficiency, convenience, and cost performance of healthcare. The amount of data handled by MIoT devices grows exponentially, which means higher exposure of sensitive data. The security and privacy of the data collected from MIoT devices, either during their transmission to a cloud or while stored in a cloud, are major unsolved concerns. This paper focuses on the security and privacy requirements related to data flow in MIoT. In addition, we make in-depth study on the existing solutions to security and privacy issues, together with the open challenges and research issues for future work.