It is estimated that 10-30 % of road fatalities are related to drowsy driving. Driver\'s drowsiness detection based on biological and vehicle signals is being studied in preventive car safety. Autonomous nervous system activity, which can be measured noninvasively from the heart rate variability (HRV) signal obtained from surface electrocardiogram, presents alterations during stress, extreme fatigue and drowsiness episodes. We hypothesized that these alterations manifest on HRV and thus could be used to detect driver\'s drowsiness. We analyzed three driving databases in which drivers presented different sleep-deprivation levels, and in which each driving minute was annotated as drowsy or awake. We developed two different drowsiness detectors based on HRV. While the drowsiness episodes detector assessed each minute of driving as "awake" or "drowsy" with seven HRV derived features (positive predictive value 0.96, sensitivity 0.59, specificity 0.98 on 3475 min of driving), the sleep-deprivation detector discerned if a driver was suitable for driving or not, at driving onset, as function of his sleep-deprivation state. Sleep-deprivation state was estimated from the first three minutes of driving using only one HRV feature (positive predictive value 0.80, sensitivity 0.62, specificity 0.88 on 30 drivers). Incorporating drowsiness assessment based on HRV signal may add significant improvements to existing car safety systems.