Alcohol use disorder (AUD) and addiction in general is characterized by failures of choice resulting in repeated drug intake despite severe negative consequences. Behavioral change is hard to accomplish and relapse after detoxification is common and can be promoted by consumption of small amounts of alcohol as well as exposure to alcohol-associated cues or stress. While those environmental factors contributing to relapse have long been identified, the underlying psychological and neurobiological mechanism on which those factors act are to date incompletely understood. Based on the reinforcing effects of drugs of abuse, animal experiments showed that drug, cue and stress exposure affect Pavlovian and instrumental learning processes, which can increase salience of drug cues and promote habitual drug intake. In humans, computational approaches can help to quantify changes in key learning mechanisms during the development and maintenance of alcohol dependence, e.g. by using sequential decision making in combination with computational modeling to elucidate individual differences in model-free versus more complex, model-based learning strategies and their neurobiological correlates such as prediction error signaling in fronto-striatal circuits. Computational models can also help to explain how alcohol-associated cues trigger relapse: mechanisms such as Pavlovian-to-Instrumental Transfer can quantify to which degree Pavlovian conditioned stimuli can facilitate approach behavior including alcohol seeking and intake. By using generative models of behavioral and neural data, computational approaches can help to quantify individual differences in psychophysiological mechanisms that underlie the development and maintenance of AUD and thus promote targeted intervention.