Highlights•Different quantitative MRI techniques offer complementary information on normal and abnormal white matter microstructure.•Of the techniques that offer microstructural information, multi-shell DWI and myelin water imaging are particularly promising in leukodystrophies.•Quantitative MRI may provide secondary outcome measures in leukodystrophy trials.•Interpretation of modelled MRI measures in terms of pathology should take into account that models are based on normal white matter and may need to be adapted for abnormal white matter.•Correlations between different MRI measures and disease severity should be further examined.