The cerebral cortex underlies our complex cognitive capabilities, yet we know little about the specific genetic loci influencing human cortical structure. To identify genetic variants, including structural variants, impacting cortical structure, we conducted a genome-wide association meta-analysis of brain MRI data from 51,662 individuals. We analysed the surface area and average thickness of the whole cortex and 34 regions with known functional specialisations. We identified 255 nominally significant loci (P [≤] 5 x 10-8); 199 survived multiple testing correction (P [≤] 8.3 x 10-10; 187 surface area; 12 thickness). We found significant enrichment for loci influencing total surface area within regulatory elements active during prenatal cortical development, supporting the radial unit hypothesis. Loci impacting regional surface area cluster near genes in Wnt signalling pathways, known to influence progenitor expansion and areal identity. Variation in cortical structure is genetically correlated with cognitive function, Parkinsons disease, insomnia, depression and ADHD.\n\nOne Sentence SummaryCommon genetic variation is associated with inter-individual variation in the structure of the human cortex, both globally and within specific regions, and is shared with genetic risk factors for some neuropsychiatric disorders.