Advances in medical and surgical care of the critically ill neonates have decreased mortality, yet a significant number of these neonates suffer from neurodevelopmental delays and failure in school. Thus, clinicians are now focusing on prevention of neurologic injury and improvement of neurocognitive outcome in these high-risk infants. Assessment of cerebral oxygenation, cerebral blood volume, and the regulation of cerebral blood flow (CBF) during the neonatal period is vital for evaluating brain health. Traditional CBF imaging methods fail, however, for both ethical and logistical reasons. In this dissertation, I demonstrate the use of non-invasive optical modalities, i.e., diffuse optical spectroscopy and diffuse correlation spectroscopy, to study cerebral oxygenation and cerebral blood flow in the critically ill neonatal population. The optical techniques utilize near-infrared (NIR) light to probe the static and dynamic physiological properties of deep tissues. Diffuse correlation spectroscopy (DCS) employs the transport of temporal correlation functions of diffusing light to extract relative changes in blood flow in biological tissues. Diffuse optical spectroscopy (DOS) employs the wavelength-dependent attenuation of NIR light to assess the concentrations of the primary chromophores in the tissue, namely oxy- and deoxy-hemoglobin. This dissertation presents both validation and clinical applications of novel diffuse optical spectroscopies in two specific critically ill neonatal populations: very-low birth weight preterm infants, and infants born with complex congenital heart defects. For validation of DCS in neonates, the blood flow index quantified by DCS is shown to correlate well with velocity measurements in the middle cerebral artery acquired by transcranial Doppler ultrasound. In patients with congenital heart defects DCS-measured relative changes in CBF due to hypercapnia agree strongly with relative changes in blood flow in the jugular veins as measured by phase-encoded velocity mapping magnetic resonance. For applications in the clinic, CO2 reactivity in patients with congenital heart defects prior to various stages of reconstructive surgery was quantified; our initial results suggest that CO2 reactivity is not systematically related to brain injury in this population. Additionally, the cerebral effects of various interventions, such as blood transfusion and sodium bicarbonate infusion, were investigated. In preterm infants, monitoring with DCS reveals a resilience of these patients to maintain constant CBF during a small postural manipulation.