This article provides a brief review of concepts of the features of the pre- and postnatal development of the central nervous system in vertebrates. Particular attention is paid to questions of the origins of neuron populations at different periods of nervous system development. Neuron and glial populations are shown to arise from different sources: neural stem cells (NSC) give rise to the neurogenic epithelium by vertical migration in the brain wall, while closer to birth, their successors give rise to cells of the so-called radial glia (RG) and intermediate precursor cells (IPC). Replenishment of the neuron population in some parts of the brain occurs as a result of tangential migration of neuroblasts from the neurogenic zones located at great distances from the final site of neuron differentiation. The processes of neuro- and gliogenesis are affected by a large number of different growth, neurotrophic, and transcription factors. Questions of the features of postnatal neurogenesis in the adult nervous system in vertebrates and the potential of using model objects for studying this process in humans are discussed. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.