In the neonatal intensive care unit (NICU), heart rate, respiratory rate, and oxygen saturation are vital signs (VS) that are continuously monitored in infants, while blood pressure is often monitored continuously immediately after birth, or during critical illness. Although changes in VS can reflect infant physiology or circadian rhythms, persistent deviations in absolute values or complex changes in variability can indicate acute or chronic pathology. Recent studies demonstrate that analysis of continuous VS trends can predict sepsis, necrotizing enterocolitis, brain injury, bronchopulmonary dysplasia, cardiorespiratory decompensation, and mortality. Subtle changes in continuous VS patterns may not be discerned even by experienced clinicians reviewing spot VS data or VS trends captured in the monitor. In contrast, objective analysis of continuous VS data can improve neonatal outcomes by allowing heightened vigilance or preemptive interventions. In this review, we provide an overview of the studies that have used continuous analysis of single or multiple VS, their interactions, and combined VS and clinical analytic tools, to predict or detect neonatal pathophysiology. We make the case that big-data analytics are promising, and with continued improvements, can become a powerful tool to mitigate neonatal diseases in the twenty-first century.