Reversing or slowing the aging process brings great promise to treat or prevent age-related disease, and targeting the hallmarks of aging is a strategy to achieve this. Epigenetics affects several if not all of the hallmarks of aging and has therefore emerged as a central target for intervention. One component of epigenetic regulation involves histone deacetylases (HDAC), which include the “classical” histone deacetylases (of class I, II, and IV) and sirtuin deacetylases (of class III). While targeting sirtuins for healthy aging has been extensively reviewed elsewhere, this review focuses on pharmacologically inhibiting the classical HDACs to promote health and longevity. We describe the theories of how classical HDAC inhibitors may operate to increase lifespan, supported by studies in model organisms. Furthermore, we explore potential mechanisms of how HDAC inhibitors may have such a strong grasp on health and longevity, summarizing their links to other hallmarks of aging. Finally, we show the wide range of age-related preclinical disease models, ranging from neurodegeneration to heart disease, diabetes to sarcopenia, which show improvement upon HDAC inhibition.