Hypertrophic cardiomyopathy (HCM) is an important cause of morbidity and mortality with both monogenic and polygenic components. We here report results from the largest HCM genome-wide association study (GWAS) and multi-trait analysis (MTAG) including 5,900 HCM cases, 68,359 controls, and 36,083 UK Biobank (UKB) participants with cardiac magnetic resonance (CMR) imaging. We identified a total of 70 loci (50 novel) associated with HCM, and 62 loci (32 novel) associated with relevant left ventricular (LV) structural or functional traits. Amongst the common variant HCM loci, we identify a novel HCM disease gene, SVIL, which encodes the actin-binding protein supervillin, showing that rare truncating SVIL variants cause HCM. Mendelian randomization analyses support a causal role of increased LV contractility in both obstructive and non-obstructive forms of HCM, suggesting common disease mechanisms and anticipating shared response to therapy. Taken together, the findings significantly increase our understanding of the genetic basis and molecular mechanisms of HCM, with potential implications for disease management.