Future smart healthcare systems—often referred to as Internet of Medical Things (IoMT) – will combine a plethora of wireless devices and applications that use wireless communication technologies to enable the exchange of healthcare data. Smart healthcare requires sufficient bandwidth, reliable and secure communication links, energy-efficient operations, and Quality of Service (QoS) support. The integration of Internet of Things (IoT) solutions into healthcare systems can significantly increase intelligence, flexibility, and interoperability. This work provides an extensive survey on emerging IoT communication standards and technologies suitable for smart healthcare applications. A particular emphasis has been given to low-power wireless technologies as a key enabler for energy-efficient IoT-based healthcare systems. Major challenges in privacy and security are also discussed. A particular attention is devoted to crowdsourcing/crowdsensing, envisaged as tools for the rapid collection of massive quantities of medical data. Finally, open research challenges and future perspectives of IoMT are presented.