Cocaine, methamphetamine and opioids are leading causes of drug abuse-related deaths worldwide. In recent decades, several studies revealed the connection between and epigenetics. Neural cells acquire epigenetic alterations that drive the onset and progress of the SUD by modifying the histone residues in brain reward circuitry. Histone modifications, especially acetylation and methylation, participate in the regulation of gene expression. These alterations, as well as other host and microenvironment factors, are associated with a serious of negative neurocognitive disfunctions in various patient populations. In this review, we highlight the evidence that substantially increase the field's ability to understand the molecular actions underlying SUD and summarize the potential approaches for SUD pharmacotherapy.© 2023 The Authors. Published by Elsevier Ltd.