Addiction is a state of compulsive drug use; despite treatment and other attempts to control drug taking, addiction tends to persist. Clinical and laboratory observations have converged on the hypothesis that addiction represents the pathological usurpation of neural processes that normally serve reward-related learning. The major substrates of persistent compulsive drug use are hypothesized to be molecular and cellular mechanisms that underlie long-term associative memories in several forebrain circuits (involving the ventral and dorsal striatum and prefrontal cortex) that receive input from midbrain dopamine neurons. Here we review progress in identifying candidate mechanisms of addiction.