Children surviving premature birth have a high risk of cognitive and learning disabilities and attention deficit. In turn, adverse outcomes are associated with persistent reductions in cerebral growth on magnetic resonance imaging (MRI). It is striking that modern care has been associated with a dramatic reduction in the risk of cystic white matter damage, but modest improvements in terms of neurodevelopmental impairment. This review will explore the hypothesis that the disability is primarily associated with impaired neural connectivity rather than cell death alone. Very preterm infants exhibit reduced thalamocortical connectivity and cortical neuroplasticity compared with term-born controls. In preterm fetal sheep, moderate cerebral ischemia with no neuronal loss, but significant diffuse failure of maturation of cortical pyramidal neurons, was associated with impaired dendritic growth and synapse formation, consistent with altered connectivity. These changes were associated with delayed decline in cortical fractional anisotropy (FA) on MRI. Supporting these preclinical findings, preterm human survivors showed similar enduring impairment of microstructural development of the cerebral cortex defined by FA, consistent with delayed formation of neuronal processes. These findings offer the promise that better understanding of impairment of neural connectivity may allow us to promote normal development and growth of the cortex after preterm birth.