Reading and writing are crucial for many aspects of modern life but up to 1 in 10 children are affected by dyslexia [1, 2], which can persist into adulthood. Family studies of dyslexia suggest heritability up to 70% [3, 4], yet no convincing genetic markers have been found due to limited study power . Here, we present a genome-wide association study representing a 20-fold increase in sample size from prior work, with 51,800 adults self-reporting a dyslexia diagnosis and 1,087,070 controls. We identified 42 independent genome-wide significant loci: 17 are in genes linked to or pleiotropic with cognitive ability/educational attainment; 25 are novel and may be more specifically associated with dyslexia. Twenty-three loci (12 novel) were validated in independent cohorts of Chinese and European ancestry. We confirmed a similar genetic aetiology of dyslexia between sexes, and found genetic covariance with many traits, including ambidexterity, but not neuroanatomical measures of language-related circuitry. Causal analyses revealed a directional effect of dyslexia on attention deficit hyperactivity disorder and bidirectional effects on socio-educational traits but these relationships require further investigation. Dyslexia polygenic scores explained up to 6% of variance in reading traits in independent cohorts, and might in future enable earlier identification and remediation of dyslexia.