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Imaging is an indispensable tool for brain tumour diagnosis, surgical planning, and follow-up. Definite diagnosis, however, often demands histopathological analysis of microscopic features of tissue samples, which have to be obtained by invasive means. A non-invasive alternative may be to probe corresponding microscopic tissue characteristics by MRI, or so called ‘microstructure imaging’. The promise of microstructure imaging is one of ‘virtual biopsy’ with the goal to offset the need for invasive procedures in favour of imaging that can guide pre-surgical planning and can be repeated longitudinally to monitor and predict treatment response. The exploration of such methods is motivated by the striking link between parameters from MRI and tumour histology, for example the correlation between the apparent diffusion coefficient and cellularity. Recent microstructure imaging techniques probe even more subtle and specific features, providing parameters associated to cell shape, size, permeability, and volume distributions. However, the range of scenarios in which these techniques provide reliable imaging biomarkers that can be used to test medical hypotheses or support clinical decisions is yet unknown. Accurate microstructure imaging may moreover require acquisitions that go beyond conventional data acquisition strategies. This review covers a wide range of candidate microstructure imaging methods based on diffusion MRI and relaxometry, and explores advantages, challenges, and potential pitfalls in brain tumour microstructure imaging.Quantitative MRI techniques can provide microstructure information in tumours.Methods for acquisition and analysis of dMRI of tumours are reviewed.Relation between MRI parameters and microscopy-detected features is discussed.Challenges in microstructure imaging of brain tumour are detailed.