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The genetic basis of brain structure and function is largely unknown. We carried out genome-wide association studies (GWAS) of 3,144 distinct functional and structural brain imaging derived phenotypes (IDPs), using imaging and genetic data from a total of 9,707 participants in UK Biobank. All subjects were imaged on a single scanner, with 6 distinct brain imaging modalities being acquired. We show that most of the IDPs are heritable and we identify patterns of coheritability within and between IDP sub-classes. We report 1,262 SNP associations with IDPs, based on a discovery sample of 8,426 subjects. Notable significant and interpretable associations include: spatially specific changes in T2* in subcortical regions associated with several genes related to iron transport and storage; spatially extended changes in white matter micro-structure and lesion volume associated with genes coding for proteins of the extracellular matrix and the epidermal growth factor; variations in pontine crossing tract organization associated with genes that regulate axon guidance and fasciculation during development; and more broadly, variations in brain imaging measures associated with 14 genes involved in development, pathway signalling and plasticity, including overlap with 6 genes contributing to transport of nutrients and minerals. Our results provide new insight into the genetic architecture of the brain with relevance to complex neurological and psychiatric disorders, as well as brain development and aging.