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In multiple sclerosis (MS), accurate in vivo characterization of the heterogeneous lesional and extra-lesional tissue pathology remains challenging. Marshalling several advanced imaging techniques — quantitative relaxation time (T1) mapping, a model-free average diffusion signal approach and four multi-shell diffusion models — this study investigates the performance of multi-shell diffusion models and characterizes the microstructural damage within (i) different MS lesion types — active, chronic active, and chronic inactive — (ii) their respective periplaque white matter (WM), and (iii) the surrounding normal-appearing white matter (NAWM). In 83 MS participants (56 relapsing-remitting, 27 progressive) and 23 age and sex-matched healthy controls (HC), we analysed a total of 317 paramagnetic rim lesions (PRL+), 232 non-paramagnetic rim lesions (PRL-), 38 contrast-enhancing lesions (CEL). Consistent with previous findings and histology, our analysis revealed the ability of advanced multi-shell diffusion models to characterize the unique microstructural patterns of CEL, and to elucidate their possible evolution into a resolving (chronic inactive) vs smoldering (chronic active) inflammatory stage. In addition, we showed that the microstructural damage extends well beyond the MRI-visible lesion edge, gradually fading out while moving outward from the lesion edge into the immediate WM periplaque and the NAWM, the latter still characterized by diffuse microstructural damage in MS vs HC. This study also emphasizes the critical role of selecting appropriate diffusion models to elucidate the complex pathological architecture of MS lesions and their periplaque. More specifically, multi-compartment diffusion models based on biophysically interpretable metrics such as neurite orientation dispersion and density (NODDI; mean auc=0.8002) emerge as the preferred choice for MS applications, while simpler models based on a representation of the diffusion signal, like diffusion tensor imaging (DTI; mean auc=0.6942), consistently underperformed, also when compared to T1 mapping (mean auc=0.73375).