In diffusion MRI (dMRI), images are sensitised to water diffusion by the application of magnetic field gradients. Cell membranes hinder the diffusional motion and thereby contribute to the contrast in dMRI. Thus, the diffusion of water molecules is used a probe of tissue microstructure. Data from dMRI is often analysed using diffusion tensor imaging (DTI), which yields image biomarkers that reflect cell density and the orientation coherence of tissue, in terms of the mean diffusivity (MD) and fractional anisotropy (FA), respectively. However, these metrics conflates multiple measures of the microstructure. In our group, we are developing a novel set of technologies for acquisition and analysis of dMRI that we collectively call multidimensional microstructure imaging (MMI). MMI takes advantage of our recent developments for dMRI that enables diffusion encoding by gradient waveforms that goes beyond previous strategies, such as so-called single diffusion encoding.