Drug craving, the desire to experience the effect(s) of a previously experienced psychoactive substance, has been hypothesized to contribute significantly to continued drug use and relapse after a period of abstinence in humans. In more theoretical terms, drug craving can be conceptualized within the framework of incentive motivational theories of behavior and be defined as the incentive motivation to self-administer a psychoactive substance. The incentive-motivational value of drugs is hypothesized to be determined by a continuous interaction between the hedonic rewarding properties of drugs (incentive) and the motivational state of the organism (organismic state). In drug-dependent individuals, the incentive-motivational value of drugs (i.e., drug craving) is greater compared to non-drug-dependent individuals due to the motivational state (i.e., withdrawal) developed with repeated drug administration. In this conceptual framework, animal models of drug craving would reflect two aspects of the incentive motivation to self-administer a psychoactive substance. One aspect would be the unconditioned incentive (reinforcing) value of the drug itself. The other aspect would be relatively independent of the direct (unconditioned) incentive value of the drug itself and could be reflected in the ability of previously neutral stimuli to acquire conditioned incentive properties that could elicit drug-seeking and drug-taking behavior. Animal models of drug craving that permit the investigation of the behavioral and neurobiological components of these two aspects of drug craving are reviewed and evaluated. The models reviewed are the progressive ratio, choice, extinction, conditioned reinforcement and second-order schedule paradigms. These animal models are evaluated according to two criteria that are established herein as necessary and sufficient criteria for the evaluation of animal models of human psychopathology: reliability and predictive validity. The development of animal models of drug craving will have heuristic value and allow a systematic investigation of the neurobiological mechanisms of craving.