Continued seeking and drinking of alcohol despite adverse legal, health, economic, and societal consequences is a central hallmark of human alcohol use disorders. This compulsive drive for alcohol, defined by resistance to adverse and deleterious consequences, represents a major challenge when attempting to treat alcoholism clinically. Thus, there has long been interest in developing pre-clinical rodent models for the compulsive drug use that characterizes drug addiction. Here, we review recent studies that have attempted to model compulsive aspects of alcohol and cocaine intake in rodents, and consider technical and conceptual issues that need to be addressed when trying to recapitulate compulsive aspects of human addiction. Aversion-resistant alcohol intake has been examined by pairing intake or seeking with the bitter tastant quinine or with footshock, and exciting recent work has used these models to identify neuroadaptations in the amygdala, cortex, and striatal regions that promote compulsive intake. Thus, rodent models do seem to reflect important aspects of compulsive drives that sustain human addiction, and will likely provide critical insights into the molecular and circuit underpinnings of aversion-resistant intake as well as novel therapeutic interventions for compulsive aspects of addiction.