Drug addiction is a complex neuropsychiatric disorder that affects a subset of the individuals who take drugs. It is characterized by maladaptive drug-seeking habits that are maintained despite adverse consequences and intense drug craving. The pathophysiology and etiology of addiction is only partially understood despite extensive research because of the gap between current preclinical models of addiction and the clinical criteria of the disorder. This review presents a brief overview, based on selected methodologies, of how behavioral models have evolved over the last 50 years to the development of recent preclinical models of addiction that more closely mimic diagnostic criteria of addiction. It is hoped that these new models will increase our understanding of the complex neurobiological mechanisms whereby some individuals switch from controlled drug use to compulsive drug-seeking habits and relapse to these maladaptive habits. Additionally, by paving the way to bridge the gap that exists between biobehavioral research on addiction and the human situation, these models may provide new perspectives for the development of novel and effective therapeutic strategies for drug addiction.