The recent global COVID-19 pandemic has revealed that the current healthcare system in modern society can hardly cope with the increased number of patients. Part of the load can be alleviated by incorporating smart healthcare infrastructure in the current system to enable patient’s remote monitoring and personalized treatment. Technological advances in communications and sensing devices have enabled the development of new, portable, and more power-efficient biomedical sensors, as well as innovative healthcare applications. Nevertheless, such applications require reliable, resilient, and secure networks. This paper aims to identify the communication requirements for mass deployment of such smart healthcare sensors by providing the overview of underlying Internet of Things (IoT) technologies. Moreover, it highlights the importance of information theory in understanding the limits and barriers in this emerging field. With this motivation, the paper indicates how data compression and entropy used in security algorithms may pave the way towards mass deployment of such IoT healthcare devices. Future medical practices and paradigms are also discussed.