Recent findings indicate that Music Therapy (MT) and Music-Based Interventions (MBIs) may reduce craving symptoms in people with Substance Use Disorders (SUD). However, MT/MBIs can lead SUD clients to recall memories associated with their drug history and the corresponding strong emotions (addiction memories). Craving is a central component of SUD, possibly linked to relapse and triggered by several factors such as the recall of memories associated with the drug experience. Therefore, to address the topic of what elements can account for an improvement in craving symptoms after MT/MBIs, we conducted a narrative review that (1) describes the brain correlates of emotionally salient autobiographical memories evoked by music, (2) outlines neuroimaging and neurophysiological studies suggesting how the experience of craving may encompass the recall of emotionally filled moments, and (3) points out the role of perineuronal nets (PNNs) in addiction memory neuroplasticity. We highlight how autobiographical memory retrieval, music-evoked autobiographical memories, and craving share similar neural activations with PNNs which represent a causal element in the processing of addiction memory. We finally conclude by considering how the neuroplastic characteristics of addiction memory might represent the ground to update and/or recalibrate, within the therapy, the emotional content related to the recall.