Brain injury in the premature infant is an extremely important problem, in part because of the large absolute number of infants affected yearly. The two principal brain lesions that underlie the neurological manifestations subsequently observed in premature infants are periventricular hemorrhagic infarction and periventricular leukomalacia. The emphases of this article are the neurology, neuropathology, and pathogenesis of these two lesions. Recent work suggests that the ultimate goal, prevention of the lesions, is potentially achievable. Periventricular hemorrhagic infarction may be preventable by prevention of germinal matrix/intraventricular hemorrhage, and periventricular leukomalacia, by detection of impaired cerebrovascular autoregulation, prevention of impaired cerebral blood flow, and interruption of the cascade to oligodendroglial cell death by such agents as free-radical scavengers.