Since the 1980s, diffusion magnetic resonance imaging (dMRI) as a magnetic resonance imaging (MRI) technique has been widely used to track the effective diffusion of water molecules, which is hindered by many obstacles (e.g., fibers or membranes), in the human brain in vivo. Because water molecules tend to diffuse slowly across white matter fibers and diffuse fast along such fibers, the use of dMRI to track water diffusion allows one to map the microstructure and organization of those white matter pathways (17). Quantitatively measuring the diffusion process is critical for a quantitative assessment of the integrity of anatomical connectivity in white matter and its association with brain functional connectivity. Its clinical applications include normal brain maturation and aging, cerebral ischemia, multiple sclerosis, epilepsy, metabolic disorders, and brain tumors, among many others. Although there are several nice review papers and monographies on dMRI (15, 5, 101, 81), this chapter was written for the readers who are interested in the theoretical underpinning of various mathematical and statistical methods associated with dMRI. Due to limitations of space, we are unable to cite all important papers in the dMRI literature.