Many animal species have been used to model certain aspects of alcohol use and addiction. However, there are complex behavioral and social features of alcohol use disorders that are not easily modeled in animal species. This review considers both the limitations and advantages of using a non-human primate to model alcohol use disorders and discusses how non-human primates can be particularly useful for studying how genetic variants interact with social factors, temperament and alcohol response as motivating factors for alcohol consumption and abstinence. Genetic variants in rhesus macaques (Macaca mulatta) that are functionally equivalent to those increasing addiction vulnerability in humans influence temperament, stress reactivity and alcohol response in addition to voluntary alcohol consumption. Non-human primate models may also have translational value for understanding of how variants within addiction and abuse vulnerability genes influence alcohol-induced neuroadaptation, neuropathology and treatment response.