This article treats the theoretical underpinnings of diffusion-tensor magnetic resonance imaging (DT-MRI), as well as experimental design and data analysis issues. We review the mathematical model underlying DT-MRI, discuss the quantitative parameters that are derived from the measured effective diffusion tensor, and describe artifacts thet arise in typical DT-MRI acquisitions. We also discuss difficulties in identifying appropriate models to describe water diffusion in heterogeneous tissues, as well as in interpreting experimental data obtained in such issues. Finally, we describe new statistical methods that have been developed to analyse DT-MRI data, and their potential uses in clinical and multi-site studies. Copyright © 2002 John Wiley & Sons, Ltd.