Alcohol use disorder (AUD) is a heritable complex behavior. Due to the highly polygenic nature of AUD, identifying genetic variants that comprise this heritable variation has proved to be challenging. With the exception of functional variants in alcohol metabolizing genes (e.g. ADH1B and ALDH2), few other candidate loci have been confidently linked to AUD. Genome-wide association studies (GWAS) of AUD and other alcohol-related phenotypes have either produced few hits with genome-wide significance or have failed to replicate on further study. These issues reinforce the complex nature of the genetic underpinnings for AUD and suggest that both GWAS studies with larger samples and additional analysis approaches that better harness the nominally significant loci in existing GWAS are needed. Here, we review approaches of interest in the post-GWAS era, including in silico functional analyses; functional partitioning of single nucleotide polymorphism heritability; aggregation of signal into genes and gene networks; and validation of identified loci, genes and gene networks in postmortem brain tissue and across species. These integrative approaches hold promise to illuminate our understanding of the biological basis of AUD; however, we recognize that the main challenge continues to be the extremely polygenic nature of AUD, which necessitates large samples to identify multiple loci associated with AUD liability.