Schizophrenia is a psychiatric disorder whose pathophysiology is largely unknown. It has a heritability of 60-80%, much of which is attributable to common risk alleles, suggesting genome-wide association studies can inform our understanding of aetiology. Here, in 69,369 people with schizophrenia and 236,642 controls, we report common variant associations at 270 distinct loci. Using fine-mapping and functional genomic data, we prioritise 19 genes based on protein-coding or UTR variation, and 130 genes in total as likely to explain these associations. Fine-mapped candidates were enriched for genes associated with rare disruptive coding variants in people with schizophrenia, including the glutamate receptor subunit GRIN2A and transcription factor SP4, and were also enriched for genes implicated by such variants in autism and developmental disorder. Associations were concentrated in genes expressed in CNS neurons, both excitatory and inhibitory, but not other tissues or cell types, and implicated fundamental processes related to neuronal function, particularly synaptic organisation, differentiation and transmission. We identify biological processes of pathophysiological relevance to schizophrenia, show convergence of common and rare variant associations in schizophrenia and neurodevelopmental disorders, and provide a rich resource of priority genes and variants to advance mechanistic studies.