Opioid use disorder (OUD) affects millions of people worldwide and the risk of developing the disorder has a significant genetic component according to twin and family studies. Identification of the genetic variants underlying this inherited risk has focused on two different methods: candidate gene studies and genome-wide association studies (GWAS). The most studied candidate genes have included the mu-opioid receptor (OPRM1), the delta-opioid receptor (OPRD1), the dopamine D2 receptor (DRD2), and brain-derived neurotrophic factor (BDNF). Variants in these genes have been associated with relatively small, but reproducible, effects on OUD risk. More recently, GWAS have identified potential associations with variants in KCNG2, KCNC1, CNIH3, APBB2, and RGMA. In total the genetic associations identified so far explain only a small portion of OUD risk. GWAS of OUD is still in the early stages when compared to studies of other psychiatric disorders, such as schizophrenia, which have found many relevant variants with small effect sizes only after large meta-analyses. Substantial increases in cohort sizes will likely be necessary in the OUD field to achieve similar results. In addition, it will be important for future studies of OUD to incorporate rare variants, epigenetics, and gene × environment interactions into models in order to better explain the observed heritability.