Every year in the United States, an estimated 500,000 babies are born preterm (before 37 completed weeks of gestation), and this number is rising, along with the recognition of brain injuries due to preterm delivery. A common underlying pathogenesis appears to be perinatal hypoxia induced by immature lung development, which causes injury to vulnerable neurons and glia. Abnormal growth and maturation of susceptible cell types, particularly neurons and oligodendrocytes, in preterm babies with very low birth weight is associated with decreased cerebral and cerebellar volumes and increases in cerebral ventricular size. Here we reconcile these observations with recent studies using models of perinatal hypoxia that show perturbations in the maturation and function of interneurons, oligodendrocytes and astroglia. Together, these findings suggest that the global mechanism by which perinatal hypoxia alters development is through a delay in maturation of affected cell types, including astroglia, oligodendroglia and neurons.