Power spectral analysis of short segments of beat-to-beat heart rate variability (PS/HRV) reveals three distinct peaks. In human PS/HRV, the high frequency (HF) band (0.15 to 0.4 Hz) is correlated with respiratory driven vagal efferent input to the sinus node. The low frequency band (LF) 0.06 to 0.15 Hz is believed to be due to baroreceptor mediated blood pressure control. Therefore, PS/HRV represents a noninvasive signature of the balance between sympathetic and parasympathetic components of the autonomic nervous system. This paper reviews the literature on the methodological issues relevant to signal processing, computational, and clinical applications of PS/HRV. Factors affecting the power in the LF and HF bands are examined in healthy controls. Recent work from several laboratories suggests that PS/HRV is a potentially powerful tool for exploring neurocardiac dysfunction in patients with a variety of cardiac and autonomic disorders. Mathematical models which simulate neurocardiac control are examined. Concerns regarding the lack of standardization between different laboratories are expressed. As the PS/HRV attains the status of a clinical diagnostic test, we hope that this review serves as a source of integrated information for researchers in this field.