The Internet of Medical Things (IoMT), an application of the Internet of Things (IoT) in the medical domain, allows data to be transmitted across communication networks. In particular, IoMT can help improve the quality of life of citizens and older people by monitoring and managing the body’s vital signs, including blood pressure, temperature, heart rate, and others. Since IoMT has become the main platform for information exchange and making high-level decisions, it is necessary to guarantee its reliability and security. The growth of IoMT in recent decades has attracted the interest of many experts. This study provides an in-depth analysis of IoT and IoMT by focusing on security concerns from different points of view, making this comprehensive survey unique compared to other existing studies. A total of 187 articles from 2010 to 2022 are collected and categorized according to the type of applications, year of publications, variety of applications, and other novel perspectives. We compare the current studies based on the above criteria and provide a comprehensive analysis to pave the way for researchers working in this area. In addition, we highlight the trends and future work. We have found that blockchain, as a key technology, has solved many problems of security, authentication, and maintenance of IoT systems due to the decentralized nature of the blockchain. In the current study, this technology is examined from the application fields’ points of view, especially in the health sector, due to its additional importance compared to other fields.