Control theory provides a powerful conceptual framework and mathematical armamentarium for modeling addictive behavior. It is particularly appropriate for repetitive, rhythmic behavior that occurs over time, such as drug use. We reframe seven selected theories of addictive behavior in control theoretic terms (heroin addiction model, opponent process theory, respondent conditioning, evolutionary theory, instrumental conditioning, incentive sensitization, and autoshaping) and provide examples of quantitative simulations for two of these models (opponent process theory and instrumental conditioning). This paper discusses theories of addiction to lay the foundation for control theoretic analyses of drug addiction phenomena, but does not review the empirical evidence for or against any particular model. These seven addiction models are then discussed in relation to the addictive phenomena for which they attempt to account and specific aspects of their feedback systems.