Diffusion MRI exploits the random motion of water molecules in biological tissues due to diffusion as a non-invasive probe of microstructure. The typical length scale of water diffusion displacement in the brain for an MRI experiment ranges from a few to a dozen of microns, that is, comparable with the sizes of the cellular compartments and barriers that restrict the diffusion process in tissues. This makes water an endogenous probe that can be used to gain insight into cell morphology and to obtain new markers of tissue microstructure. This chapter introduces the molecular basis upon which diffusion MRI of the brain relies and discusses the physical principles that enable the sensitisation of MRI signals to the Brownian motion of water. Moreover, the chapter describes a common approach for diffusion imaging, known as diffusion tensor imaging (DTI), alongside with several practical points concerned with the acquisition of diffusion-weighted imaging data with modern MRI systems. DTI is a popular method that offers a set of rotationally invariant indices of molecular diffusion. These have shown great sensitivity to pathology in several neurological conditions, but are limited by relatively low specificity. Complementary approaches extend the technique to gain a deeper insight into cytoarchitecture, striving for novel non-invasive imaging markers that characterise pathology and normal development at the cellular scale.