At present, the whole world is transitioning to the fourth industrial revolution, or Industry 4.0, representing the transition to digital, fully automated environments, and cyber-physical systems. Industry 4.0 comprises many different technologies and innovations, which are being implemented in many different sectors. In this review, we focus on the healthcare or medical domain, where healthcare is being revolutionized. The whole ecosystem is moving towards Healthcare 4.0, through the application of Industry 4.0 methodologies. Many technical and innovative approaches have had an impact on moving the sector towards the 4.0 paradigm. We focus on such technologies, including Internet of Things, Big Data Analytics, blockchain, Cloud Computing, and Artificial Intelligence, implemented in Healthcare 4.0. In this review, we analyze and identify how their applications function, the currently available state-of-the-art technologies, solutions to current challenges, and innovative start-ups that have impacted healthcare, with regards to the Industry 4.0 paradigm.