Neonatal hypoxic-ischemic insults are a significant cause of pediatric encephalopathy, developmental delays, and spastic cerebral palsy. Although the developing brain's plasticity allows for remarkable self-repair, severe disruption of normal myelination and cortical development upon neonatal brain injury are likely to generate life-persisting sensory-motor and cognitive deficits in the growing child. Currently, no treatments are available that can address the long-term consequences. Thus, regenerative medicine appears as a promising avenue to help restore normal developmental processes in affected infants. Stem cell therapy has proven effective in promoting functional recovery in animal models of neonatal hypoxic-ischemic injury and therefore represents a hopeful therapy for this unmet medical condition. Neural stem cells derived from pluripotent stem cells or fetal tissues as well as umbilical cord blood and mesenchymal stem cells have all shown initial success in improving functional outcomes. However, much still remains to be understood about how those stem cells can safely be administered to infants and what their repair mechanisms in the brain are. In this review, we discuss updated research into pathophysiological mechanisms of neonatal brain injury, the types of stem cell therapies currently being tested in this context, and the potential mechanisms through which exogenous stem cells might interact with and influence the developing brain.