Aging brings dysregulation of various processes across organs and tissues often stemming in part from stochastic damage to individual cells over time. Aging-related changes in the brain lead to cognition deficits and can impact quality of life. The molecular basis of neuronal aging remains poorly understood. This work uses a combination of single-nucleus RNA sequencing, single-cell whole-genome sequencing, and spatial transcriptomics to identify transcriptomic and genomic changes in the prefrontal cortex of the human brain across life span, from infancy to centenarian. Infant-specific cell clusters had enriched expression of neurodevelopmental genes, indicating incomplete development at birth. Oligodendrocyte precursor cell proportions were highest in infants and depleted in adult and elderly brains while oligodendrocytes were almost absent in infants and enriched in older brains. Certain subclasses of inhibitory neurons demonstrated increased transcriptional variability during aging along with decreased expression of the canonical marker genes. Elderly brains demonstrated common downregulation of cell-essential homeostatic genes that function in ribosomes, transport, and metabolism during aging across cell types. Conversely, the expression of neuron-specific genes generally remains stable throughout life. Expression of specific DNA repair genes decreased in aging, including genes implicated in generating brain somatic mutations. Furthermore, we detected gene-length-specific somatic mutation rates that shape the transcriptomic landscape of the aged human brain. These findings elucidate critical aspects of human brain aging, shedding light on transcriptomic and genomic dynamics.