The diverse cerebral consequences of preterm birth create significant challenges for understanding pathogenesis or predicting later outcome. Instead of focusing on describing effects common to the group, comparing individual infants against robust normative data offers a powerful alternative to study brain maturation. Here we used Gaussian process regression to create normative curves characterizing brain volumetric development in 274 term-born infants, modeling for age at scan and sex. We then compared 89 preterm infants scanned at term-equivalent age with these normative charts, relating individual deviations from typical volumetric development to perinatal risk factors and later neurocognitive scores. To test generalizability, we used a second independent dataset comprising of 253 preterm infants scanned using different acquisition parameters and scanner. We describe rapid, nonuniform brain growth during the neonatal period. In both preterm cohorts, cerebral atypicalities were widespread, often multiple, and varied highly between individuals. Deviations from normative development were associated with respiratory support, nutrition, birth weight, and later neurocognition, demonstrating their clinical relevance. Group-level understanding of the preterm brain disguises a large degree of individual differences. We provide a method and normative dataset that offer a more precise characterization of the cerebral consequences of preterm birth by profiling the individual neonatal brain.