Drug addiction can be seen as a disorder of maladaptive learning characterized by relapse. Therefore, disrupting drug-related memories could be an approach to improving therapies for addiction. Pioneering studies over the last two decades have revealed that consolidated memories are not static, but can be reconsolidated after retrieval, thereby providing candidate pathways for the treatment of addiction. The limbic–corticostriatal system is known to play a vital role in encoding the drug memory engram. Specific structures within this system contribute differently to the process of memory reconsolidation, making it a potential target for preventing relapse. In addition, as molecular processes are also active during memory reconsolidation, amnestic agents can be used to attenuate drug memory. In this review, we focus primarily on the brain structures involved in storing the drug memory engram, as well as the molecular processes involved in drug memory reconsolidation. Notably, we describe reports regarding boundary conditions constraining the therapeutic potential of memory reconsolidation. Furthermore, we discuss the principles that could be employed to modify stored memories. Finally, we emphasize the challenge of reconsolidation-based strategies, but end with an optimistic view on the development of reconsolidation theory for drug relapse prevention.