Automatic medical diagnosis is an emerging center of interest in computer vision as it provides unobtrusive objective information on a patient's condition. The face, as a mirror of health status, can reveal symptomatic indications of specific diseases. Thus, the detection of facial abnormalities or atypical features is at upmost importance when it comes to medical diagnostics. This survey aims to give an overview of the recent developments in medical diagnostics from facial images based on computer vision methods. Various approaches have been considered to assess facial symptoms and to eventually provide further help to the practitioners. However, the developed tools are still seldom used in clinical practice, since their reliability is still a concern due to the lack of clinical validation of the methodologies and their inadequate applicability. Nonetheless, efforts are being made to provide robust solutions suitable for healthcare environments, by dealing with practical issues such as real-time assessment or patients positioning. This survey provides an updated collection of the most relevant and innovative solutions in facial images analysis. The findings show that with the help of computer vision methods, over 30 medical conditions can be preliminarily diagnosed from the automatic detection of some of their symptoms. Furthermore, future perspectives, such as the need for interdisciplinary collaboration and collecting publicly available databases, are highlighted.