Since its introduction in the mid-1980s, diffusion magnetic resonance imaging (MRI), which measures the random motion of water molecules in tissues, revealing their microarchitecture, has become a pillar of modern neuroimaging. Its main clinical domain has been the diagnosis of acute brain stroke and neurogical disorders, but it is also used in the body for the detection and management of cancer lesions. It can also produce stunning maps of white matter tracks in the brain, with the potential to aid in the understanding of some psychiatric disorders. However, in order to exploit fully the potential of this method, a deeper understanding of the mechanisms that govern the diffusion of water in tissues is needed.