The development of MR imaging techniques during the past decade has enabled researchers to use MR imaging as a noninvasive tool for evaluating structural and physiologic states in biologic tissues by measuring the diffusion process of water molecules. More recently, diffusion tensor MR imaging (DTI) technique based on the dependency of molecular diffusion on the orientation of white matter fiber tracts has been used to analyze the trajectory, shape, fiber structure, location, topology and connectivity of neuronal fiber pathways in living humans. Numerous efforts have been made by MR physicists, brain scientists, and medical doctors to advance MR techniques and computer-based algorithms which result in more accurate quantification of diffusion tensor and the generation of white matter fiber tract maps and to determine the pathophysiology of brain disease by DTI and useful clinical applications of DTI. In this article, we describe the tensor theory used to characterize molecular diffusion in white matter and a process of measuring tensor elements using diffusion-sensitive MR images to fiber mapping. We then provide review of current literature and some clinical examples that have been published and are on-going.