Phase synchronization between two weakly coupled oscillators has been studied in chaotic systems for a long time. However, it is difficult to unambiguously detect such synchronization in experimental data from complex physiological systems. In this paper we review our study of phase synchronization between heartbeat and respiration in 150 healthy subjects during sleep using an automated procedure for screening the synchrograms. We found that this synchronization is significantly enhanced during non-rapid-eye-movement (non-REM) sleep (deep sleep and light sleep) and is reduced during REM sleep. In addition, we show that the respiration signal can be reconstructed from the heartbeat recordings in many subjects. Our reconstruction procedure, which works particularly well during non-REM sleep, allows the detection of cardiorespiratory synchronization even if only heartbeat intervals were recorded.