We humans are constantly preoccupied with our health and physiological status. From precise measurements such as the 12-lead electrocardiograms recorded in hospitals, we have moved on to mobile acquisition devices, now as versatile as smart-watches and smart-phones. Established signal processing techniques do not cater to the particularities of mobile biomedical health monitoring applications. Moreover, although our capabilities to acquire data are growing, many underlying physiological phenomena remain poorly understood. This thesis focuses on two aspects of biomedical signal processing. First, we investigate the physiological basis of the relationship between cardiac and breathing biosignals. Second, we propose a methodology to understand and use this relationship in health monitoring applications. Part I of this dissertation examines the physiological background of the cardio-respiratory relationship and indexes based on this relationship. We propose a methodology to extract the respiratory sinus arrhythmia (RSA), which is an important aspect of this relationship. Furthermore, we propose novel indexes incorporating dynamics of the cardio-respiratory relationship, using the RSA and the phase lag between RSA and breathing. We then evaluate, systematically, existing and novel indexes under known autonomic stimuli. We demonstrate our indexes to be viable additions to the existing ones, thanks to their performance and physiological merits. Part II focuses on real-time and instantaneous methods for the estimation of the breathing parameters from cardiac activity, which is an important application of the cardio-respiratory relationship. The breathing rate is estimated from electrocardiogram and imaging photoplethysmogram recordings, using two dedicated filtering schemes, one of which is novel. Our algorithm measures this important vital rhythm in a truly real-time manner, with significantly shorter delays than existing methods. Furthermore, we identify situations, in which an important assumption regarding the estimation of breathing parameters from cardiac activity does not hold, and draw a road-map to overcome this problem. In Part III, we use indexes and methodology developed in Parts I and II in two applications for mobile health monitoring, namely, emotion recognition and sleep apnea detection from cardiac and breathing biosignals. Results on challenging datasets show that the cardio-respiratory indexes introduced in the present thesis, especially those related to the phase lag between RSA and breathing, are successful for emotion recognition and sleep apnea detection. The novel indexes reveal to be complementary to previous ones, and bring additional insight into the physiological basis of emotions and apnea episodes. To summarize, the techniques proposed in this thesis help to bypass shortcomings of previous approaches in the understanding and the estimation of cardio-respiratory coupling in real-life mobile health monitoring.