The development of interventions aimed at improving healthspan is one of the priority tasks for the academic and public health authorities. It is also the main objective of a novel branch in biogerontological research, geroscience. According to the geroscience concept, targeting aging is an effective way to combat age-related disorders. Since aging is an exceptionally complex process, system-oriented integrated approaches seem most appropriate for such an interventional strategy. Given the high plasticity and adaptability of the epigenome, epigenome-targeted interventions appear highly promising in geroscience research. Pharmaceuticals targeted at mechanisms involved in epigenetic control of gene activity are actively developed and implemented to prevent and treat various aging-related conditions such as cardiometabolic, neurodegenerative, inflammatory disorders, and cancer. In this review, we describe the roles of epigenetic mechanisms in aging; characterize enzymes contributing to the regulation of epigenetic processes; particularly focus on epigenetic drugs, such as inhibitors of DNA methyltransferases and histone deacetylases that may potentially affect aging-associated diseases and longevity; and discuss possible caveats associated with the use of epigenetic drugs.