Research on the concept of craving may lead to better understanding of the biobehavioural circuitries that contribute to the complexity of alcohol use disorders (AUDs). The experiences described as craving or desire to drink are often associated with physical responses such as increased salivation and heart rate, and alteration of stress hormones, as well as psychological responses such as anxiety and depression. Greater craving has been associated with an increased probability of alcohol relapse. Reversal of craving, which is understood as a symptom of protracted abstinence, offers the possibility of preventing relapses and treating alcoholism. Various medications have been studied to establish whether they are able to reduce craving; however, the results obtained from clinical studies have been inconsistent. Here, we review the interdisciplinary models developed to evaluate craving, then the different approaches used to assess and measure craving and, finally, the medications utilized and tested to lessen craving in patients suffering from AUDs.