Monitoring vital signs through unobtrusive means is a goal which has attracted a lot of attention in the past decade. This review provides a systematic and comprehensive review over the current state of the field of ambient and unobtrusive cardiorespiratory monitoring. To this end, nine different sensing modalities which have been in the focus of current research activities are covered: capacitive electrocardiography, seismo- and ballistocardiography, reflective photoplethysmography (PPG) and PPG imaging, thermography, methods relying on laser or radar for distance-based measurements, video motion analysis, as well as methods using high-frequency electromagnetic fields. Current trends in these subfields are reviewed. Moreover, we systematically analyze similarities and differences between these methods with respect to the physiological and physical effects they sense as well as the resulting implications. Finally, future research trends for the field as a whole are identified.