Ambient Intelligence (AmI) is a new paradigm in information technology aimed at empowering people's capabilities by means of digital environments that are sensitive, adaptive, and responsive to human needs, habits, gestures, and emotions. This futuristic vision of daily environment will enable innovative human-machine interactions characterized by pervasive, unobtrusive, and anticipatory communications. Such innovative interaction paradigms make AmI technology a suitable candidate for developing various real life solutions, including in the healthcare domain. This survey will discuss the emergence of AmI techniques in the healthcare domain, in order to provide the research community with the necessary background. We will examine the infrastructure and technology required for achieving the vision of AmI, such as smart environments and wearable medical devices. We will summarize the state-of-the-art artificial intelligence (AI) methodologies used for developing AmI system in the healthcare domain, including various learning techniques (for learning from user interaction), reasoning techniques (for reasoning about users' goals and intensions), and planning techniques (for planning activities and interactions). We will also discuss how AmI technology might support people affected by various physical or mental disabilities or chronic disease. Finally, we will point to some of the successful case studies in the area and we will look at the current and future challenges to draw upon the possible future research paths.