In an attempt to better understand the pharmacological and neurobiological determinants of drug addiction, researchers have begun to build mathematical and computational models of drug self-administration. Quantitative pharmacological models have been developed to describe the acquisition of drug self-administration behavior and the maintenance of drug use behavior. However, models that describe behavior acquisition are unable to explain behavior maintenance, and vice versa. Recently, computational modeling has been used to develop more neurobiologically realistic models with the potential to explain drug self-administration across all major behavioral stages (i.e., initiation, escalation and maintenance)and across a wide range of reinforcement contingencies. Intrigued by the apparent irrational behavior of drug addicts, researchers from a wide range of scientific disciplines have formulated a plethora of theoretical schemes over the years to understand addiction. However, most of these models are qualitative in nature and are formulated using terms that are often ill-defined. As a result, the empirical validity of these models has been difficult to test rigorously, which has served to generate more controversy than clarity. In this context, as in other scientific fields, mathematical and computational modeling may contribute to the development of more testable and rigorous models of addiction. Recently, several researchers have begun to simulate drug self-administration behavior in an attempt to better understand the pharmacological and neurobiological determinants of drug addiction. This article stems from a 2006 College on Problems of Drug Dependence (CPDD) workshop and includes a few examples of mathematical and computational models of drug self-administration in rodents that illustrate the contribution of mathematical modeling to our understanding of the pharmacological and neurobiological factors in drug self-administration.