Neonatal hypoxic-ischemic encephalopathy (HIE) is a common cause of long-term neurological disability in children. Despite advances in supportive care, no treatments for HIE are available at present. The potential use of stem/progenitor cell therapies for neuroprotection or regeneration of the damaged adult brain has been evaluated in several preclinical studies, and the most promising results are now being tested in clinical trials. In recent years, the use of stem/progenitor cell transplantation in animal models of HIE has also been evaluated in several laboratories. It was shown that human umbilical cord blood mononuclear cells and mesenchymal stem/progenitor cells may have a therapeutic potential through multiple mechanisms acting locally in the central nervous system and possibly in peripheral organs of hypoxic-ischemic animals. Neural stem/progenitor cells (NSCs) have also been transplanted in animal models of HIE, migrating long distances to ischemic brain areas and differentiating into neurons. The results of these studies have raised important questions that must be addressed before these findings can be translated to the bedside. In this review, we give a critical overview of the different studies published up to now, and we discuss the endogenous regenerative potential of NSCs of the newborn brain when challenged by an HIE insult. We also discuss the use of cell therapies for the encephalopathy of prematurity.