Hypertrophic cardiomyopathy (HCM) is a common, serious, genetic heart disorder. Rare pathogenic variants in sarcomere genes cause HCM, but with unexplained phenotypic heterogeneity. Moreover, most patients do not carry such variants. We report a genome-wide association study of 2,780 cases and 47,486 controls that identified 12 genome-wide-significant susceptibility loci for HCM. Single-nucleotide polymorphism heritability indicated a strong polygenic influence, especially for sarcomere-negative HCM (64% of cases; h2g = 0.34 ± 0.02). A genetic risk score showed substantial influence on the odds of HCM in a validation study, halving the odds in the lowest quintile and doubling them in the highest quintile, and also influenced phenotypic severity in sarcomere variant carriers. Mendelian randomization identified diastolic blood pressure (DBP) as a key modifiable risk factor for sarcomere-negative HCM, with a one standard deviation increase in DBP increasing the HCM risk fourfold. Common variants and modifiable risk factors have important roles in HCM that we suggest will be clinically actionable.