The exponential growth in digital technology is leading us to a future in which all things and all people are connected all the time, something we refer to as The Infinite Network (TIN), which will cause profound changes in every industry. Here, we focus on the impact it will have in healthcare. TIN will change the essence of healthcare to a data-driven continuous approach as opposed to the event-driven discrete approach used today. At a micro or individual level, smart sensing will play a key role, in the form of embedded sensors, wearable sensors, and sensing from smart medical devices. At a macro or aggregate level, healthcare will be provided by Intelligent Telehealth Networks that evolve from the telehealth networks that are available today. Traditional telemedicine has delivered remote care to patients in the area where doctors are not readily available, but has not achieved at large scale. New advanced networks will deliver care at a much larger scale. The long-term future requires intelligent hybrid networks that combine artificial intelligence with human intelligence to provide continuity of care at higher quality and lower cost than is possible today.