Rather than a singular event that suddenly appears during adulthood, adult neurogenesis has long been recognized as the continuation of postnatal neurogenic activity. During the first postnatal weeks, significant cellular changes occur within and adjacent to germinal matrices of the subventricular zone and dentate gyrus. The majority of granule cells are generated during this period. In addition, radial glia are transformed into astrocyte-like stem cells, the ependymal layer is formed, and the highest rates of angiogenesis, gliogenesis and myelination are observed. The first postnatal weeks are critical as the brain growth rate is maximal, and changes during this period can have a great impact on neurogenesis levels and overall brain function later in life. This review chronicles cellular changes and some of the clinically relevant dysregulations that can occur during the postnatal period, and discusses the possible impact of these changes on neurogenesis and cognitive function later in life.