The arrival of the Internet of Things (IoT) and its numerous applications is revolutionizing all the sectors in which it is being integrated. This project focuses on the application of the Internet of Things in the field of medicine, the so-called Internet of Medical Things (IoMT), starting by analyzing its evolution from the first telemetry systems to the current telemedicine. This project also studies some wearable devices applied to medicine that have already been implanted in our society. Besides, it examines its architecture and its applications. In addition to this, emerging technologies such as radio frequency identification (RFID) or the use of Big Data in the analysis of data in medicine are also analyzed. We will see how they are used, what types there are and some of their different applications. In order to apply all these technological systems correctly in the medical field, certain global and regional standards and protocols must be followed, which are also examined in this paper. Due to the massive increase of collected data and devices connected to the networks, this project studies the possible threats faced by patients, the security measures applied nowadays and the different security and privacy certifications in the medical field established both in the European Union and the United States. Finally, the main challenges that the IoMT will face in the future are listed and evaluated. As a conclusion, the difficulties that the IoMT technologies will have in order to be truly integrated in hospitals and in our healthcare system are analyzed, as well as why their use is not yet fully implemented.