Heart failure (HF) management is challenging due to high clinical heterogeneity of this disease which makes patients responding differently to evidence-based standard therapy established by the current reductionist approach. Better understanding of the genetic and epigenetic interactions may clarify molecular signatures underlying maladaptive responses in HF, including metabolic shift, myocardial injury, fibrosis, and mitochondrial dysfunction. DNA methylation, histone modifications and micro-RNA (miRNAs) may be major epigenetic players in the pathogenesis of HF. DNA hypermethylation of the kruppel-like factor 15 (KLF15) gene plays a key role in switching the failing heart from oxidative to glycolytic metabolism. Moreover, hypomethylation at H3K9 promoter level of atrial natriuretic peptide (ANP) and brain natriuretic peptide (BNP) genes also leads to reactivation of fetal genes in man. The role of miRNAs has been investigated in HF patients undergoing heart transplantation, for whom miR-10a, miR-155, miR-31, and miR-92 may be putative useful prognostic biomarkers. Recently, higher RNA methylation levels have been observed in ischemic human hearts, opening the era of “epitranscriptome” in the pathogenesis of HF. Currently, hydralazine, statins, apabetalone, and omega-3 polyunsatured fatty acids (PUFA) are being tested in clinical trials to provide epigenetic-driven therapeutic interventions. Moreover, network-oriented analysis could advance current medical practice by focusing on protein–protein interactions (PPIs) perturbing the “cardiac” interactome. In this review, we provide an epigenetic map of maladaptive responses in HF patients. Furthermore, we propose the “EPi-transgeneratIonal network mOdeling for STratificatiOn of heaRt Morbidity” (EPIKO-STORM), a clinical research strategy offering novel opportunities to stratify the natural history of HF.