Adult neurogenesis, comprising the generation, differentiation and integration of new neurons in the mature brain, has emerged as a dynamic area of research over decades. The discovery of adult neurogenesis was a paradigm shift to comprehend mechanisms underlying brain plasticity, cognitive function, and neurological disorders. This review deliberates significant findings from articles published over four decades on adult neurogenesis, highlighting key milestones, methodological advances, and controversies that have shaped our comprehension of the phenomenon of adult neurogenesis. Early skepticism gave way to a rich body of evidence via various reliable approaches. Studies on neurogenic niches, microenvironmental factors, molecular regulators, and functional implications have uncovered the involvement of adult neurogenesis in learning, memory, mood, and even neurological and neurodegenerative conditions. Despite significant progress, several questions still need to be answered, including the exact contributions of new neurons to brain function, their integration into existing circuits, and the impact of enhancing adult neurogenesis in the human hippocampus. While the existence of robust neurogenesis in the adult and aged human hippocampus is yet to be confirmed, this review highlights evidence from a significant number of studies supporting the persistence of hippocampal neurogenesis during adulthood and aging in humans, including in some neurological conditions, such as epilepsy and Alzheimer's disease. Nonetheless, additional large-scale studies using single cell-RNA-seq, single nucleus-RNA-seq, and spatial transcriptomics are critical to validate the presence and contribution of hippocampal neurogenesis in the pathophysiology of various neurological and neurodegenerative conditions at different stages of the disease. There is also a need to develop standardized protocols for analyzing postmortem hippocampal tissues for cellular and molecular analyses.