Non-invasive assessment of intercompartment water exchange may be of importance to characterize pathologies which are subject to changes in membrane permeability either caused by the malignancy or as an effect of intervention. Conventional diffusion MRI is not specific to water exchange since it cannot separate the effects of exchange and restricted diffusion. For this purpose, advanced diffusion strategies based on a double-diffusion encoding have been developed to disentangle them. In this work, diffusion-based magnetic resonance methods and applications for the measurement of intercompartment exchange are reviewed.