The majority of brain growth occurs during the first two years of life, much occurring in-utero prior to birth at 40 weeks’ gestational age, and a full understanding of human brain development must include this early period of rapid development. The characterization of early brain development is particularly important in infants who are born prematurely. Preterm birth affects around 5% of births in industrialised countries and its consequences contribute to significant individual, medical and social problems. The principle morbidity among survivors is neurological, resulting from the profound effect of preterm birth on the developing brain: half of all infants born at less than 25 weeks have neurodevelopmental impairment at 30 months of age, and in less immature infants, neuropsychiatric problems are common in the teenage years. The anatomical correlates of functional disorders are, however, poorly characterized. Using state-of-the-art MR imaging it is nowadays possible to study the brain development and maturation process in infants born prematurely from as young as 25 weeks onwards. Recent advances in MR imaging also enable the acquisition of high-resolution fetal images. This allows us to study the brain development in-utero as well as ex-utero. In this talk we describe the computational challenges in the analysis of these images. In particular we describe how non-rigid registration can be used in cross-sectional and longitudinal studies to quantify brain development and growth between the last trimester of pregnancy and early childhood.