To increase our understanding of drug addiction--notably its pharmacological and neurobiological determinants--researchers have begun to formulate computational models of drug self-administration. Currently, one can roughly distinguish between three classes of models which all have in common to attribute to brain dopamine signaling a key role in addiction. The first class of models contains quantitative pharmacological models that describe the influence of pharmacokinetic and pharmacodynamic factors on drug self-administration. These models fail, however, to explain how the drug self-administration behavior is acquired and how it eventually becomes rigid and compulsive with extended drug use. Models belonging to the second class circumvent some of these limitations by modeling how drug use usurps the function of dopamine in reinforcement learning and action selection. However, despite their behavioral plausibility, these latter models lack neurobiological plausibility and ignore the potential role of opponent processes in addiction. The third class of models attempts to surmount these pitfalls by providing a more realistic picture of the midbrain dopamine circuitry and of the complex action of drugs of abuse in the output of this circuitry. Here we provide a brief overview of these different models to illustrate the potential contribution of mathematical modeling to our understanding of the neurobiology of drug addiction.