Left-right asymmetry of the human brain is one of its cardinal features, and also a complex, multivariate trait. Decades of research have suggested that brain asymmetry may be altered in psychiatric disorders. However, findings have been inconsistent and often based on small sample sizes. There are also open questions surrounding which structures are asymmetrical on average in the healthy population, and how variability in brain asymmetry relates to basic biological variables such as age and sex. Over the last 4 years, the ENIGMA-Laterality Working Group has published six studies of gray matter morphological asymmetry based on total sample sizes from roughly 3,500 to 17,000 individuals, which were between one and two orders of magnitude larger than those published in previous decades. A population-level mapping of average asymmetry was achieved, including an intriguing fronto-occipital gradient of cortical thickness asymmetry in healthy brains. ENIGMA's multi-dataset approach also supported an empirical illustration of reproducibility of hemispheric differences across datasets. Effect sizes were estimated for gray matter asymmetry based on large, international, samples in relation to age, sex, handedness, and brain volume, as well as for three psychiatric disorders: autism spectrum disorder was associated with subtly reduced asymmetry of cortical thickness at regions spread widely over the cortex; pediatric obsessive-compulsive disorder was associated with altered subcortical asymmetry; major depressive disorder was not significantly associated with changes of asymmetry. Ongoing studies are examining brain asymmetry in other disorders. Moreover, a groundwork has been laid for possibly identifying shared genetic contributions to brain asymmetry and disorders.