In this review we discuss the evidence that drug addiction, defined as a maladaptive compulsive habit, results from the progressive subversion by addictive drugs of striatum-dependent operant and Pavlovian learning mechanisms that are usually involved in the control over behaviour by stimuli associated with natural reinforcement. Although mainly organized through segregated parallel cortico-striato-pallido-thalamo-cortical loops involved in motor or emotional functions, the basal ganglia, and especially the striatum, are key mediators of the modulation of behavioural responses, under the control of both action-outcome and stimulus-response mechanisms, by incentive motivational processes and Pavlovian associations. Here we suggest that protracted exposure to addictive drugs recruits serial and dopamine-dependent, striato-nigro-striatal ascending spirals from the nucleus accumbens to more dorsal regions of the striatum that underlie a shift from action-outcome to stimulus-response mechanisms in the control over drug seeking. When this progressive ventral to dorsal striatum shift is combined with drug-associated Pavlovian influences from limbic structures such as the amygdala and the orbitofrontal cortex, drug seeking behaviour becomes established as an incentive habit. This instantiation of implicit sub-cortical processing of drug-associated stimuli and instrumental responding might be a key mechanism underlying the development of compulsive drug seeking and the high vulnerability to relapse which are hallmarks of drug addiction.