Histone deacetylases (HDAC) catalyze the removal of acetylation modifications on histones and non-histone proteins, which regulates gene expression and other cellular processes. HDAC inhibitors (HDACi), approved anti-cancer agents, emerge as a potential new therapy for heart diseases. Cardioprotective effects of HDACi are observed in many preclinical animal models of heart diseases. Genetic mouse models have been developed to understand the role of each HDAC in cardiac functions. Some of the findings are controversial. Here, we provide an overview of how HDACi and HDAC impact cardiac functions under physiological or pathological conditions. We focus on studies of zinc-dependent classical HDACs, emphasizing disease conditions involving cardiac hypertrophy, myocardial infarction (MI), ischemic reperfusion (I/R) injury, and heart failure. In particular, we review how non-biased omics studies can help our understanding of the mechanisms underlying the cardiac effects of HDACi and HDAC.