A recent preliminary, single-case report suggested that baclofen not only reduces but may completely suppress craving in alcohol-dependent individuals. The current article summarizes the neurobiological basis of drug craving, and the pharmacological targets that have been shown to be involved in modulating such craving. The potential usefulness of agents that suppress craving is discussed. However, beyond individual case reports, no evidence is available to indicate that targeting a single neurobiological pathway will be sufficient to completely suppress craving in unselected individuals. Nevertheless, subgroups that carry specific characteristics associated with single receptor dysfunction might benefit from a targeted treatment. Further research is needed to enable clinicians to detect these subgroups.