Alcoholism (alcohol dependence and alcohol use disorder, AUD) is quintessentially behavioral in nature. AUD is behaviorally and genetically complex. This review discusses behavioral assessment of alcohol sensitivity, tolerance, dependence, withdrawal, and reinforcement. The focus is on using laboratory animal models to explore genetic contributions to individual differences in alcohol responses. Rodent genetic animal models based on selective breeding for high vs low alcohol response, and those based on the use of inbred strains, are reviewed. Genetic strategies have revealed the complexity of alcohol responses where genetic influences on multiple alcohol-related behaviors are mostly discrete. They have also identified areas where genetic influences are consistent across behavioral assays and have been used to model genetic differences among humans at different risk for AUD.