In recent years, time-varying inhomogeneous point process models have been introduced for assessment of instantaneous heartbeat dynamics as well as specific cardiovascular control mechanisms and hemodynamics. Assessment of the model\'s statistics is established through the Wiener-Volterra theory and a multivariate autoregressive (AR) structure. A variety of instantaneous cardiovascular metrics, such as heart rate (HR), heart rate variability (HRV), respiratory sinus arrhythmia (RSA), and baroreceptor-cardiac reflex (baroreflex) sensitivity (BRS), are derived within a parametric framework and instantaneously updated with adaptive and local maximum likelihood estimation algorithms. Inclusion of second-order non-linearities, with subsequent bispectral quantification in the frequency domain, further allows for definition of instantaneous metrics of non-linearity. We here present a comprehensive review of the devised methods as applied to experimental recordings from healthy subjects during propofol anesthesia. Collective results reveal interesting dynamic trends across the different pharmacological interventions operated within each anesthesia session, confirming the ability of the algorithm to track important changes in cardiorespiratory elicited interactions, and pointing at our mathematical approach as a promising monitoring tool for an accurate, non-invasive assessment in clinical practice. We also discuss the limitations and other alternative modeling strategies of our point process approach.