The purpose of this article is to explain how the random walks of water molecules undergoing diffusion in living tissue may be exploited to garner information on the white matter of the human brain and its connections. We discuss the concepts underlying diffusion-weighted (DW) imaging, and diffusion tensor imaging before exploring fibre tracking, or tractography, which aims to reconstruct the three-dimensional trajectories of white matter fibres non-invasively. The two main classes of algorithm - deterministic and probabilistic tracking - are compared and example results are presented. We then discuss methods to resolve the 'crossing fibre' issue which presents a problem when using the tensor model to characterize diffusion behaviour in complex tissue. Finally, we detail some of the issues that remain to be resolved before we can reliably characterize connections of the living human brain in vivo.