Drug addiction is a progressive, relapsing disease comprised of interlocking stages of disordered motivation. Numerous animal models describing various stages of the addiction process have been developed over the past few decades, providing considerable advantages for the modeling of drug addiction compared with other complex psychiatric disease states. Escalation of drug self-administration has emerged as a widely accepted operant conditioning model of excessive drug intake. We further argue here that drug-escalated animals represent a comprehensive model of addiction according to the manifestations of behavioral neuroadaptations resulting directly or indirectly from excessive drug consumption. In particular, drug-escalated animals exhibit a host of symptoms in line with multiple Diagnostic and Statistical Manual of Mental Disorders criteria for substance dependence, which can be summarized as an emergence of uncontrollable drug-taking and drug-seeking behaviors as a consequence of within-circuit and between-circuit neuroadaptations. Such a transition from impulsive drug sampling to compulsive intake represents a highly valid conceptualization of the addiction timeline in humans, and further investigation of persistent or near-permanent (e.g. epigenetic) neuroadaptations generated by operant drug intake escalation models will continue to provide mechanisms and therapeutic interventions for reversing the aberrant neuroplasticity underlying addiction.