The inner surfaces of the human heart are covered by a complex network of muscular strands that is thought to be a remnant of embryonic development. The function of these trabeculae in adults and their genetic architecture are unknown. Here we performed a genome-wide association study to investigate image-derived phenotypes of trabeculae using the fractal analysis of trabecular morphology in 18,096 participants of the UK Biobank. We identified 16 significant loci that contain genes associated with haemodynamic phenotypes and regulation of cytoskeletal arborization3,4. Using biomechanical simulations and observational data from human participants, we demonstrate that trabecular morphology is an important determinant of cardiac performance. Through genetic association studies with cardiac disease phenotypes and Mendelian randomization, we find a causal relationship between trabecular morphology and risk of cardiovascular disease. These findings suggest a previously unknown role for myocardial trabeculae in the function of the adult heart, identify conserved pathways that regulate structural complexity and reveal the influence of the myocardial trabeculae on susceptibility to cardiovascular disease.