Hypoxic-ischemic encephalopathy (HIE) is a major cause of newborn brain damage stemming from a lack of oxygenated blood flow in the neonatal period. Twenty-five to fifty percent of asphyxiated infants who develop HIE die in the neonatal period, and about sixty percent of survivors develop long-term neurological disabilities. From the first minutes to months after the injury, a cascade of events occurs, leading to blood-brain barrier (BBB) opening, neuronal death and inflammation. To date, the only approach proposed in some cases is therapeutic hypothermia (TH). Unfortunately, TH is only partially protective and is not applicable to all neonates. This review synthesizes current knowledge on the basic molecular mechanisms of brain damage in hypoxia-ischemia (HI) and on the different therapeutic strategies in HI that have been used and explores a major limitation of unsuccessful therapeutic approaches.