According to the World Health Organization, approximately six in 100 people suffer from post-traumatic stress disorder (PTSD) at some point in their lives. PTSD is a mental disorder with a set of symptoms observed in a person following exposure to a life-threatening event or witness a death. The primary characteristic of PTSD is the persistence over time of certain symptoms: flashbacks, traumatic nightmares, acute stress, and symptoms of depression. In a stressful situation, the whole body goes into tension. This has an energy cost and affects the voice, breathing, daily gestures, and face, which are referred to in this survey article as external symptoms. The diagnosis of PTSD is based on the Diagnostic and Statistical Manual of Mental Disorders (DSM) classification using standard questionnaires where the patient self-reports their condition based on their symptoms. Indeed, these questionnaires have several limitations and give an imprecise diagnosis. Sensors and wearable-based technologies can play a key role in improving the diagnosis, the prognosis, and the assistance of PTSD. Recently, computer-aided diagnosis (CAD) systems have been proposed for PTSD detection based on external symptoms and brain activity using video and electroencephalography (EEG) sensors. To the best of our knowledge, this is the first survey article that gives a literature overview of machine-learning-based approaches for PTSD diagnosis using video and EEG sensors. In addition, a comparison between existing approaches and a discussion about the potential avenues for future PTSD research is provided.