Conventional MR imaging techniques are sensitive to pathologic changes of the brain and spinal cord seen in MS, but they lack specificity for underlying axonal and myelin integrity. By isolating the signal contribution from different tissue compartments, newly developed advanced multicompartment diffusion MR imaging models have the potential to detect specific tissue subtypes and associated injuries with increased pathologic specificity. These models include neurite orientation dispersion and density imaging, diffusion basis spectrum imaging, multicompartment microscopic diffusion MR imaging with the spherical mean technique, and models enabled through high-gradient diffusion MR imaging. In this review, we provide an appraisal of the current literature on the physics principles, histopathologic validation, and clinical applications of each of these techniques in both brains and spinal cords of patients with MS. We discuss limitations of each of the methods and directions that future research could take to provide additional validation of their roles as biomarkers of axonal and myelin injury in MS.