Genome-wide association (GWA) can elucidate molecular genetic bases for human individual differences in complex phenotypes that include vulnerability to addiction. Here, we review (a) evidence that supports polygenic models with (at least) modest heterogeneity for the genetic architectures of addiction and several related phenotypes; (b) technical and ethical aspects of importance for understanding GWA data, including genotyping in individual samples versus DNA pools, analytic approaches, power estimation, and ethical issues in genotyping individuals with illegal behaviors; (c) the samples and the data that shape our current understanding of the molecular genetics of individual differences in vulnerability to substance dependence and related phenotypes; (d) overlaps between GWA data sets for dependence on different substances; and (e) overlaps between GWA data for addictions versus other heritable, brain-based phenotypes that include bipolar disorder, cognitive ability, frontal lobe brain volume, the ability to successfully quit smoking, neuroticism, and Alzheimer's disease. These convergent results identify potential targets for drugs that might modify addictions and play roles in these other phenotypes. They add to evidence that individual differences in the quality and quantity of brain connections make pleiotropic contributions to individual differences in vulnerability to addictions and to related brain disorders and phenotypes. A "connectivity constellation" of brain phenotypes and disorders appears to receive substantial pathogenic contributions from individual differences in a constellation of genes whose variants provide individual differences in the specification of brain connectivities during development and in adulthood. Heritable brain differences that underlie addiction vulnerability thus lie squarely in the midst of the repertoire of heritable brain differences that underlie vulnerability to other common brain disorders and phenotypes.