Radio Frequency Identification (RFID) technology is gaining significant momentum for tracking and tracing patients. The existing solutions for patient traceability are mostly centralized and closed-loop (effective only in small-scale RFID tracking applications). Lately, there has been a tendency to tag surrounding physical objects and to adopt various solutions that enable them to communicate with one another and with Information and Communications Technology (ICT) systems. This leads to a new concept named the Internet of Things (IoT), in which objects are associated with useful digital information. IoT can bring multiple benefits to healthcare through the use of information from distributed resources such as dedicated devices, RFID tags, sensors/detectors, intelligent equipment, etc. IoT is likely to have impact on many applications in healthcare subfields such as, elderly and patient care, medical supply chain, logistic, asset management, drug counterfeit detection, etc. This paper deals with aspects related to technologies used in healthcare, and with the various challenges healthcare faces during transition from RFID to IoT.