The inheritance of substance abuse, including opioid abuse, may be influenced by genetic and non-genetic factors related to the environment, such as stress and socioeconomic status. These non-genetic influences on the heritability of a trait can be attributed to epigenetics. Epigenetic inheritance can result from modifications passed down from the mother, father, or both, resulting in either maternal, paternal, or parental epigenetic inheritance, respectively. These epigenetic modifications can be passed to the offspring to result in multigenerational, intergenerational, or transgenerational inheritance. Human and animal models of opioid exposure have shown generational effects that result in molecular, developmental, and behavioral alterations in future generations.