This paper reviews our current understanding of the long-term effects of obstructive sleep apnea (OSA) on cardiovascular autonomic function in humans, focusing directly on the knowledge derived from noninvasive measurements of heart rate, beat-to-beat blood pressure (BP), and respiration during wakefulness and sleep. While heart rate variability (HRV) as a means of autonomic assessment has become ubiquitous, there are serious limitations with the conventional time-domain and spectral methods of analysis. These shortcomings can be overcome with the application of a multivariate mathematical model that incorporates BP, respiration and other external factors as physiological sources of HRV. Using this approach, we have found that: (a) both respiratory-cardiac coupling and baroreflex dynamics are impaired in OSA; (b) continuous positive airway pressure therapy partially restores autonomic function; (c) baroreflex gain, which increases during sleep in normals, remains unchanged or decreases in OSA subjects; and (d) the autonomic changes that accompany transient arousal from NREM sleep in normals are largely absent in patients with OSA.