Healthcare 4.0 is a recent e-health paradigm associated with the concept of Industry 4.0. It provides approaches to achieving precision medicine that delivers healthcare services based on the patient’s characteristics. Moreover, Healthcare 4.0 enables telemedicine, including telesurgery, early predictions, and diagnosis of diseases. This represents an important paradigm for modern societies, especially with the current situation of pandemics. The release of the fifth-generation cellular system (5G), the current advances in wearable device manufacturing, and the recent technologies, e.g., artificial intelligence (AI), edge computing, and the Internet of Things (IoT), are the main drivers of evolutions of Healthcare 4.0 systems. To this end, this work considers introducing recent advances, trends, and requirements of the Internet of Medical Things (IoMT) and Healthcare 4.0 systems. The ultimate requirements of such networks in the era of 5G and next-generation networks are discussed. Moreover, the design challenges and current research directions of these networks. The key enabling technologies of such systems, including AI and distributed edge computing, are discussed.