Studying how the healthy human brain develops is important to understand early pathological mechanisms and to assess the influence of fetal or perinatal events on later life. Brain development relies on complex and intermingled mechanisms especially during gestation and first post-natal months, with intense interactions between genetic, epigenetic and environmental factors. Although the baby's brain is organized early on, it is not a miniature adult brain: regional brain changes are asynchronous and protracted, i.e. sensory-motor regions develop early and quickly, whereas associative regions develop later and slowly over decades. Concurrently, the infant/child gradually achieves new performances, but how brain maturation relates to changes in behavior is poorly understood, requiring non-invasive in vivo imaging studies such as magnetic resonance imaging (MRI). Two main processes of early white matter development are reviewed: (1) establishment of connections between brain regions within functional networks, leading to adult-like organization during the last trimester of gestation, (2) maturation (myelination) of these connections during infancy to provide efficient transfers of information. Current knowledge from post-mortem descriptions and in vivo MRI studies is summed up, focusing on T1- and T2-weighted imaging, diffusion tensor imaging, and quantitative mapping of T1/T2 relaxation times, myelin water fraction and magnetization transfer ratio.