Cortical asymmetry is a ubiquitous feature of brain organization that is subtly altered in some neurodevelopmental disorders, yet we lack knowledge of how its development proceeds across life in health. Achieving consensus on the precise cortical asymmetries in humans is necessary to uncover the developmental timing of asymmetry and the extent to which it arises through genetic and later influences in childhood. Here, we delineate population-level asymmetry in cortical thickness and surface area vertex-wise in seven datasets and chart asymmetry trajectories longitudinally across life (4-89 years; observations = 3937; 70% longitudinal). We find replicable asymmetry interrelationships, heritability maps, and test asymmetry associations in large-scale data. Cortical asymmetry was robust across datasets. Whereas areal asymmetry is predominantly stable across life, thickness asymmetry grows in childhood and peaks in early adulthood. Areal asymmetry is low-moderately heritable (max h ~19%) and correlates phenotypically and genetically in specific regions, indicating coordinated development of asymmetries partly through genes. In contrast, thickness asymmetry is globally interrelated across the cortex in a pattern suggesting highly left-lateralized individuals tend towards left-lateralization also in population-level right-asymmetric regions (and vice versa), and exhibits low or absent heritability. We find less areal asymmetry in the most consistently lateralized region in humans associates with subtly lower cognitive ability, and confirm small handedness and sex effects. Results suggest areal asymmetry is developmentally stable and arises early in life through genetic but mainly subject-specific stochastic effects, whereas childhood developmental growth shapes thickness asymmetry and may lead to directional variability of global thickness lateralization in the population.