Continuous health monitoring using wireless body area networks (WBANs) of wearable, epidermal and implantable medical devices is envisioned as a transformative approach to healthcare. Rapid advances in biomedical sensors, low-power electronics, and wireless communications have brought this vision to the verge of reality. However, key challenges still remain to be addressed. This paper surveys the current state-of-the-art in the area of wireless sensors for medical applications. Specifically, it focuses on presenting the recent advancements in wearable, epidermal and implantable technologies, and discusses reported ways of powering up such sensors. Furthermore, this paper addresses the challenges that exist in the various Open Systems Interconnection (OSI) layers and illustrates future research areas concerning the utilization of wireless sensors in healthcare applications.