Hemispheric asymmetry is a cardinal feature of human brain organization. Altered brain asymmetry has also been linked to some cognitive and neuropsychiatric disorders. Here the ENIGMA consortium presents the largest ever analysis of cerebral cortical asymmetry and its variability across individuals. Cortical thickness and surface area were assessed in MRI scans of 17,141 healthy individuals from 99 datasets worldwide. Results revealed widespread asymmetries at both hemispheric and regional levels, with a generally thicker cortex but smaller surface area in the left hemisphere relative to the right. Regionally, asymmetries of cortical thickness and/or surface area were found in the inferior frontal gyrus, transverse temporal gyrus, parahippocampal gyrus, and entorhinal cortex. These regions are involved in lateralized functions, including language and visuospatial processing. In addition to population-level asymmetries, variability in brain asymmetry was related to sex, age, and brain size (indexed by intracranial volume). Interestingly, we did not find significant associations between asymmetries and handedness. Finally, with two independent pedigree datasets (N = 1,443 and 1,113, respectively), we found several asymmetries showing modest but highly reliable heritability. The structural asymmetries identified, and their variabilities and heritability provide a reference resource for future studies on the genetic basis of brain asymmetry and altered laterality in cognitive, neurological, and psychiatric disorders.