Stress and mental health have become major concerns worldwide. Research has already extensively investigated physiological signals as quantitative and continuous markers of stress. In recent years the focus of the field has shifted from the laboratory to the ambulatory environment. We provide an overview of physiological stress detection in laboratory settings with a focus on identifying physiological sensing priorities, including electrocardiogram, skin conductance and electromyogram, and the most suitable machine learning techniques, of which the choice depends on the context of the application. Additionally, an overview is given of new challenges ahead to move towards the ambulant environment, including the influence of physical activity, lower signal quality due to motion artifacts, the lack of a stress reference and the subject-dependent nature of the physiological stress response. Finally, several recommendations for future research are listed, focusing on large scale, longitudinal trials across different population groups and just-in-time interventions to move towards disease prevention and interception.