Escalation of drug use, a hallmark of drug dependence, has traditionally been interpreted as reflecting the development of tolerance to the drug’s effects. However, on the basis of animal behavioral data, several groups have recently proposed alternative explanations, i.e. that such an escalation of drug use might not be based on (1) tolerance, but rather be indicative of (2) sensitization to the drug’s reinforcing effect, (3) reward allostasis, (4) an increase in the incentive salience of drug-associated stimuli, (5) an increase in the reinforcing strength of the drug reinforcer relative to alternative reinforcers, or (6) habit formation. From the pharmacological perspective, models 1–3 allow predictions about the change in the shape of drug dose-effect curves that are based on mathematically defined models governing receptor-ligand interaction and signal transduction. These predictions are tested in the present review, which also describes the other currently championed models for drug use escalation and other components of apparent ‘reinforcement’ (in its original meaning, like ‘tolerance’ or ‘sensitization’, a purely descriptive term). It evaluates the animal experimental approaches employed to support or prove the existence of each of the models and reinforcement components, and recapitulates the clinical evidence, which strongly suggests that escalation of drug use is predominantly based on an increase in the frequency of intoxication events rather than an increase in the dose taken at each intoxication event. Two apparent discrepancies in animal experiments are that (a) sensitization to overall reinforcement has been found more often for psychostimulants than for opioids, and that (b) tolerance to the reinforcing and other effects has been observed more often for opioids than for cocaine. These discrepancies are resolved by the finding that cocaine levels seem to be more tightly regulated at submaximum reinforcing levels than opioid levels are. Consequently, animals self-administering opioids are more likely to expose themselves to higher above-threshold doses than animals self-administering psychostimulants, rendering the development of tolerance to opioids more likely than tolerance to psychostimulants. The review concludes by making suggestions on how to improve the current behavioral experimental approaches.