People take addictive drugs to elevate mood, but with repeated use these drugs produce serious unwanted effects, which can include tolerance to some drug effects, sensitization to others, and an adapted state - dependence - which sets the stage for withdrawal symptoms when drug use stops. The most serious consequence of repetitive drug taking, however, is addiction: a persistent state in which compulsive drug use escapes control, even when serious negative consequences ensue. Addiction is characterized by a long-lasting risk of relapse, which is often initiated by exposure to drug-related cues. Substantial progress has been made in understanding the molecular and cellular mechanisms of tolerance, dependence and withdrawal, but as yet we understand little of the neural substrates of compulsive drug use and its remarkable persistence. Here we review evidence for the possibility that compulsion and its persistence are based on a pathological usurpation of molecular mechanisms that are normally involved in memory.