Cortical asymmetry is a ubiquitous feature of brain organization that is altered in neurodevelopmental disorders and aging. Achieving consensus on cortical asymmetries in humans is necessary to uncover the genetic-developmental mechanisms that shape them and factors moderating cortical lateralization. Here, we delineate population-level asymmetry in cortical thickness and surface area vertex-wise in 7 datasets and chart asymmetry trajectories across life (4-89 years; observations = 3937; 70% longitudinal). We reveal asymmetry interrelationships, heritability, and test associations in UK Biobank (N=∼37,500). Cortical asymmetry was robust across datasets. Whereas areal asymmetry is predominantly stable across life, thickness asymmetry grows in development and declines in aging. Areal asymmetry correlates in specific regions, whereas thickness asymmetry is globally interrelated across cortex and suggests high directional variability in global thickness lateralization. Areal asymmetry is moderately heritable (max h2SNP ∼19%), and phenotypic correlations are reflected by high genetic correlations, whereas heritability of thickness asymmetry is low. Finally, we detected an asymmetry association with cognition and confirm recently-reported handedness links. Results suggest areal asymmetry is developmentally stable and arises in early life, whereas developmental changes in thickness asymmetry may lead to directional variability of global thickness lateralization. Our results bear enough reproducibility to serve as a standard for future brain asymmetry studies.