Alcohol use disorder (AUD) represents a serious public health issue, and discovery of new therapies is a pressing necessity. Alcohol exposure has been widely demonstrated to modulate epigenetic mechanisms, such as histone acetylation/deacetylation balance, in part via histone deacetylase (HDAC) inhibition. Epigenetic factors have been suggested to play a key role in AUD. To date, 18 different mammalian HDAC isoforms have been identified, and these have been divided into four classes. Since recent studies have suggested that both epigenetic mechanisms underlying AUD and the efficacy of HDAC inhibitors (HDACIs) in different animal models of AUD may involve class I HDACs, we herein report the development of class I HDACIs, including information regarding their structure, potency, and selectivity. More effort is required to improve the selectivity, pharmacokinetics, and toxicity profiles of HDACIs to achieve a better understanding of their efficacy in reducing addictive behavior.