Phase synchronization between coupled oscillators occurs in many natural systems. Since it is difficult to unambiguously detect such weak nonlinear effects in experimental data, several methods have been proposed for this purpose. We have systematically optimized and compared five approaches, studying phase synchronization of heartbeat and respiration in 180 healthy subjects during sleep and in 1400 cardiac patients that had a myocardial infarction one week earlier. We find that cardio-respiratory phase synchronization is significantly increased during light and deep sleep at night compared with daytime, but drastically decreased during rapid-eye-movement (REM) sleep. Furthermore, cardiac patients with synchronization below a certain limit have a three-fold increased risk of death within the next two years – a predictor independent of standard cardiology parameters. We compare with results for surrogate data generated by Fourier phase randomization and real data with artificial inaccuracies. For an interpretation of the sleep-stage differences, we draw relations to long-term correlations in heartbeat, respiration and brain-wave time series (determined by detrended fluctuation analysis), which occur mainly during wakefulness and REM sleep. In the second part of the presentation the focus will be on synchronization properties of brain waves recorded by electro encephalography (EEG). Studying phase synchronization within and across brain hemispheres we find that Parkinson's disease causes a significant decrease of phase synchronization – a possible early indicator for the progressing disease. Different physiological states and activities are reflected in characteristic networks of brain-wave synchronization. A further characterization of the non-linear interactions between brain-wave oscillators can be obtained from the technique of amplitude and frequency cross-modulation analysis, which relates oscillations in different EEG bands and distinguishes positive and negative modulation.