Alcohol addiction is a chronic relapsing brain disease characterized by an impaired ability to stop or control alcohol use despite adverse consequences. A main challenge of addiction treatment is to prevent relapse, which occurs in more than >50% of newly abstinent patients with alcohol disorder within 3 months. In people suffering from alcohol addiction, stressful events, drug-associated cues and contexts, or re-exposure to a small amount of alcohol trigger a chain of behaviors that frequently culminates in relapse. In this review, we first present the preclinical models that were developed for the study of alcohol seeking behavior, namely the reinstatement model of alcohol relapse and compulsive alcohol seeking under a chained schedule of reinforcement. We then provide an overview of the neurobiological findings obtained using these animal models, focusing on the role of opioids systems, corticotropin-release hormone and neurokinins, followed by dopaminergic, glutamatergic, and GABAergic neurotransmissions in alcohol seeking behavior.