Substance use disorders (SUDs) are prevalent and result in an array of negative consequences. They are influenced by genetic factors (h2 = ~50%). Recent years have brought substantial progress in our understanding of the genetic etiology of SUDs and related traits. The present review covers the current state of the field for SUD genetics, including the epidemiology and genetic epidemiology of SUDs, findings from the first-generation of SUD genome-wide association studies (GWAS), cautions about translating GWAS findings to clinical settings, and suggested prioritizations for the next wave of SUD genetics efforts. Recent advances in SUD genetics have been facilitated by the assembly of large GWAS samples, and the development of state-of-the-art methods modeling the aggregate effect of genome-wide variation. These advances have confirmed that SUDs are highly polygenic with many variants across the genome conferring risk, the vast majority of which are of small effect. Downstream analyses have enabled finer resolution of the genetic architecture of SUDs and revealed insights into their genetic relationship with other psychiatric disorders. Recent efforts have also prioritized a closer examination of GWAS findings that have suggested non-uniform genetic influences across measures of substance use (e.g. consumption) and problematic use (e.g. SUD). Additional highlights from recent SUD GWAS include the robust confirmation of loci in alcohol metabolizing genes (e.g. ADH1B and ALDH2) affecting alcohol-related traits, and loci within the CHRNA5-CHRNA3-CHRNB4 gene cluster influencing nicotine-related traits. Similar successes are expected for cannabis, opioid, and cocaine use disorders as sample sizes approach those assembled for alcohol and nicotine.