Chronic exposure to drugs of abuse produces profound changes in gene expression and neural activity associated with drug-seeking and taking behavior. Dysregulation of opioid receptor gene expression is commonly observed across a variety of abused substances including opioids, cocaine, and alcohol. Early studies in cultured cells showed that the spatial and temporal gene expression of opioid receptors are regulated by epigenetic mechanisms including DNA and histone modifications and non-coding RNAs. Accumulating evidence indicate that drugs of abuse can modulate opioid receptor gene expression by targeting various epigenetic regulatory networks. Based on current cellular and animal models of substance use disorder and clinical evidence, this review summarizes how chronic drug exposure alters the gene expression of mu, delta, kappa, and nociceptin receptors via DNA and histone modifications. The influence of drugs of abuse on epigenetic modulators, such as non-coding RNAs and transcription factors, is also presented. Finally, the therapeutic potential of manipulating epigenetic processes as an avenue to treat substance use disorder is discussed.