Congenital heart defects (CHD) are the most common type of birth defect, affecting approximately 30,000 children each year, one third of whom require cardiac surgery in their first year of life. Surgical advances have improved the cardiac outcomes for these children, and since the majority of these patients now reach school age, the research focus has shifted to address neurodevelopmental difficulties of survivors. A key physiological factor appears to be the high prevalence of hypoxic-ischemic white mater brain injury observed in these children. The exact timing of the injury occurrence, however, is difficult to ascertain due to limitations of the imaging modalities employed for this fragile, infant population. This thesis develops and explores the use of diffuse optical spectroscopy techniques for investigation of the risk factors for hypoxic-ischemic brain injury in these infants. The optical techniques utilize near-infrared (NIR) light and the diffusion approximation to model light transport in order to probe the static and dynamic properties of tissue. Frequency-domain diffuse optical spectroscopy (FD-DOS) is a technology, similar to widely used near-infrared spectroscopy (NIRS), that permits quantification of tissue oxygen saturation and total hemoglobin concentration. Diffuse correlation spectroscopy (DCS) is a relatively newer technique, centered on an idea similar to dynamic light scattering, which enables quantification of blood flow. Both FD-DOS and DCS are used in this research. The experiments presented in this thesis explore a variety of biophysics and biomedical questions. Arguably, the most important clinical findings to emerge from this dissertation are new risk factors associated with brain injury in infants with a certain form of CHD called hypoplastic left heart syndrome (HLHS). Using the aforementioned optical techniques, we found that longer time-to-surgery, lower cerebral oxygen saturation, and higher cerebral blood flow measured on the morning of surgery were associated with the risk of acquiring post-operative brain injury in this cohort. The results are novel for the community and shift our understanding of when these neonates are most at risk for acquiring brain injury. Most importantly, these results and the technology developed should improve current clinical care of this patient population.