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Congenital heart diseases often involve maldevelopment of the evolutionarily recent right heart chamber. To gain insight into right heart structure and function, we fine-tuned deep learning models to recognize the right atrium, right ventricle and pulmonary artery, measuring right heart structures in 40,000 individuals from the UK Biobank with magnetic resonance imaging. Genome-wide association studies identified 130 distinct loci associated with at least one right heart measurement, of which 72 were not associated with left heart structures. Loci were found near genes previously linked with congenital heart disease, including NKX2-5, TBX5/TBX3, WNT9B and GATA4. A genome-wide polygenic predictor of right ventricular ejection fraction was associated with incident dilated cardiomyopathy (hazard ratio, 1.33 per standard deviation; P = 7.1 × 10) and remained significant after accounting for a left ventricular polygenic score. Harnessing deep learning to perform large-scale cardiac phenotyping, our results yield insights into the genetic determinants of right heart structure and function.