Early human brain development constitutes a sequence of intricate processes resulting in the ontogeny of functionally operative neural circuits. Developmental trajectories of early brain network formation are genetically programmed and can be modified by epigenetic and environmental influences. Such alterations may exert profound effects on neurodevelopment, potentially persisting throughout the lifespan. This review focuses on the critical period of fetal and early postnatal brain development. Here we collate findings from neuroimaging studies, with a particular focus on functional MRI research that interrogated early brain network development in both health and high-risk or disease states. First, we will provide an overview of the developmental processes that take place from the embryonic period through early infancy in order to contextualize brain network formation. Second, functional brain network development in the typically developing brain will be discussed. Third, we will touch on prenatal and perinatal risk factors that may interfere with the trajectories of functional brain wiring, including prenatal substance exposure, maternal mental illness and preterm birth. Collectively, studies have revealed the blueprint of adult human brain organization to be present in the neonatal brain. Distinct attributes of human brain architecture have even been detected in the developing fetal brain from as early as 24 postconceptional weeks. During postnatal brain development, the brain's wiring pattern is further sculpted and modulated to become the full facsimile of the adult human brain, with functional brain network refinement being more rigorous than structural brain network maturation. Advances in neuroimaging techniques have paved the way towards a comprehensive understanding of the maturational pathways of brain network development and of how early developmental adversity may affect these trajectories. Such insights are fundamental for our understanding of human brain functioning, for early identification of infants at risk, as well as for future neuroprotective strategies.