This review discusses the evidence for the hypothesis that the development of drug addiction can be understood in terms of interactions between Pavlovian and instrumental learning and memory mechanisms in the brain that underlie the seeking and taking of drugs. It is argued that these behaviours initially are goal-directed, but increasingly become elicited as stimulus–response habits by drug-associated conditioned stimuli that are established by Pavlovian conditioning. It is further argued that compulsive drug use emerges as the result of a loss of prefrontal cortical inhibitory control over drug seeking habits. Data are reviewed that indicate these transitions from use to abuse to addiction depend upon shifts from ventral to dorsal striatal control over behaviour, mediated in part by serial connectivity between the striatum and midbrain dopamine systems. Only some individuals lose control over their drug use, and the importance of behavioural impulsivity as a vulnerability trait predicting stimulant abuse and addiction in animals and humans, together with consideration of an emerging neuroendophenotype for addiction are discussed. Finally, the potential for developing treatments for addiction is considered in light of the neuropsychological advances that are reviewed, including the possibility of targeting drug memory reconsolidation and extinction to reduce Pavlovian influences on drug seeking as a means of promoting abstinence and preventing relapse.