Brain abnormality in surviving premature infants is associated with an enormous amount of neurodevelopmental disability, manifested principally by cognitive, behavioral, attentional, and socialization deficits, most commonly with only relatively modest motor deficits. The most recognized contributing neuropathology is cerebral white matter injury. The thesis of this review is that acquired cerebellar abnormality is a relatively less recognized but likely important cause of neurodevelopmental disability in small premature infants. The cerebellar disease may be primarily destructive (eg, hemorrhage, infarction) or primarily underdevelopment. The latter appears to be especially common and relates to a particular vulnerability of the cerebellum of the small premature infant. Central to this vulnerability are the extraordinarily rapid and complex developmental events occurring in the cerebellum. The disturbance of development can be caused either by direct adverse effects on the cerebellum, especially the distinctive transient external granular layer, or by indirect remote trans-synaptic effects. This review describes the fascinating details of cerebellar development, with an emphasis on events in the premature period, the major types of cerebellar abnormality acquired during the premature period, their likely mechanisms of occurrence, and new insights into the relation of cerebellar disease in early life to subsequent cognitive/behavioral/attentional/socialization deficits.