Drug addiction is a chronic relapsing brain disease, characterized by compulsive drug use. Despite the fact that drug addiction affects millions of people worldwide, treatments for this disorder are limited in number and efficacy. In our opinion, understanding the neural underpinnings of drug addiction would open new avenues for the development of innovative treatments for this disorder. Based on an awareness that drug use and drug reward do not equal drug addiction, there has been increasing interest in developing animal models of addiction that mimick the loss of control over drug use more closely than existing models aimed at studying drug reward. The present review provides an overview of animal studies of compulsive drug use and the neural mechanisms involved. First, the employed models are summarized, with a particular emphasis on models of escalation of drug use and resistance to punishment. Next, we discuss mechanisms within the (ventral and dorsal) striatum and (central) amygdala that have recently been implicated in the compulsive seeking and taking of alcohol and cocaine. The studies discussed here provide a promising line of research that will advance our knowledge of the neural circuits involved in the self-destructive behavior that characterizes drug addiction.