Morphology underlies subdivision of the primary/heritable sarcomeric cardiomyopathies (CMs) into hypertrophic (HCM) and dilated (DCM). Next-generation DNA-sequencing (NGS) has identified important disease-variants, improving CM diagnosis, management, genetic screening, and prognosis. Although monogenic (Mendelian) analyses directly point at downstream studies, they disregard coexisting genomic variations and gene-by-gene interactions molding detailed CM-phenotypes. In-place of polygenic models, in accounting for observed defective genotype-phenotype correlations, fuzzy concepts having gradations of significance and unsharp domain-boundaries are invoked, including pleiotropy, genetic-heterogeneity, incomplete penetrance, and variable expressivity. HCM and DCM undoubtedly entail cooperativity of unidentified/elusive causative genomic-variants. Modern genomics can exploit comprehensive electronic/digital health records, facilitating consideration of multifactorial variant-models. Genome-wide association studies entailing high-fidelity solid-state catheterization, multimodal-imaging, molecular cardiology, systems biology and bioinformatics, will decipher accurate genotype-phenotype correlations and identify novel therapeutic-targets, fostering personalized medicine/cardiology. This review surveys successes and challenges of genetic/genomic approaches to CMs, and their impact on current and future clinical care.