The use of spoken and written language is a capacity that is unique to humans. Individual differences in reading- and language-related skills are influenced by genetic variation, with twin-based heritability estimates of 30-80%, depending on the trait. The relevant genetic architecture is complex, heterogeneous, and multifactorial, and yet to be investigated with well-powered studies. Here, we present a multicohort genome-wide association study (GWAS) of five traits assessed individually using psychometric measures: word reading, nonword reading, spelling, phoneme awareness, and nonword repetition, with total sample sizes ranging from 13,633 to 33,959 participants aged 5-26 years (12,411 to 27,180 for those with European ancestry, defined by principal component analyses). We identified a genome-wide significant association with word reading (rs11208009, p=1.098 × 10−8) independent of known loci associated with intelligence or educational attainment. All five reading-/language-related traits had robust SNP-heritability estimates (0.13–0.26), and genetic correlations between them were modest to high. Using genomic structural equation modelling, we found evidence for a shared genetic factor explaining the majority of variation in word and nonword reading, spelling, and phoneme awareness, which only partially overlapped with genetic variation contributing to nonword repetition, intelligence and educational attainment. A multivariate GWAS was performed to jointly analyse word and nonword reading, spelling, and phoneme awareness, maximizing power for follow-up investigation. Genetic correlation analysis of multivariate GWAS results with neuroimaging traits identified association with cortical surface area of the banks of the left superior temporal sulcus, a brain region with known links to processing of spoken and written language. Analysis of evolutionary annotations on the lineage that led to modern humans showed enriched heritability in regions depleted of Neanderthal variants. Together, these results provide new avenues for deciphering the biological underpinnings of these uniquely human traits.