The striatum and thalamus are subcortical structures intimately involved in addiction. The morphology and microstructure of these have been studied in murine models of cocaine addiction (CA), showing an effect of drug use, but also chronological age in morphology. Human studies using non-invasive magnetic resonance imaging (MRI) have shown inconsistencies in volume changes, and have also shown an age effect. In this exploratory study, we used MRI-based volumetric and novel shape analysis, as well as a novel fast diffusion kurtosis imaging sequence to study the morphology and microstructure of striatum and thalamus in crack CA compared to matched healthy controls (HCs), while investigating the effect of age and years of cocaine consumption. We did not find significant differences in volume and mean kurtosis (MKT) between groups. However, we found significant contraction of nucleus accumbens in CA compared to HCs. We also found significant age-related changes in volume and MKT of CA in striatum and thalamus that are different to those seen in normal aging. Interestingly, we found different effects and contributions of age and years of consumption in volume, displacement and MKT changes, suggesting that each measure provides different but complementing information about morphological brain changes, and that not all changes are related to the toxicity or the addiction to the drug. Our findings suggest that the use of finer methods and sequences provides complementing information about morphological and microstructural changes in CA, and that brain alterations in CA are related cocaine use and age differently.