This review provides an overview of animal models of acquisition of drug reinforcement by discussing research findings from studies that used drugs such as cocaine, methamphetamine (METH), phencyclidine, and nicotine, as well as several routes of drug self-administration (SA). Theoretical perspectives are given for the acquisition models indicating that the animal models are valid predictors of human -behavior. Common organismic factors that contribute to the acquisition of drug abuse are also discussed, such as sex, hormonal influences, innate preference for sweet substances, impulsivity of choice, impaired inhibition, and avidity for physical activity. Differential rates of acquisition of drug SA in rats selectively bred for high and low sweet intake, ethanol intake, or avoidance responding are also discussed. Environmental factors such as enriched versus impoverished conditions, and the effect of behavioral economic factors related to drug abuse (e.g., effort, cost/reinforcement) are also considered. Pharmacological factors have also been found to influence acquisition, such as prenatal exposure to drugs, and potential treatment drug can reduce the rates of acquisition in animal models. Interrelations among factors are described, and their implications are summarized. This review adds to previous accounts of acquisition by shifting the emphasis from analysis of the process of acquisition of drug-taking to an assessment of the major factors that are influential in the initiation and acceleration of this process. The goal is to present translatable findings from animal research that are useful for informing prevention of drug abuse in humans.